(2x-3)°+(3+4x)•(x+5)=82

To solve the equation \((2x-3)^\circ + (3 + 4x) \cdot (x + 5) = 82\), let's first clarify the notation. It seems the "°" might signify an operation or might indicate an angle in a trigonometric context—if that's not the case, please clarify. Assuming the first term is simply part of the equation and proceeding with algebraic solving, we proceed as follows: 1. **Expand the equation**: \[ (3 + 4x)(x + 5) = 3x + 15 + 4x^2 + 20x = 4x^2 + 23x + 15 \] 2. **Combine everything**: Bringing everything together we get: \[ (2x - 3) + (4x^2 + 23x + 15) = 82 \] which simplifies to: \[ 4x^2 + 23x + 15 + 2x - 3 = 82 \] 3. **Simplifying further**: \[ 4x^2 + 25x + 12 = 82 \] Now subtract 82 from both sides to set the equation to 0: \[ 4x^2 + 25x + 12 - 82 = 0 \] \[ 4x^2 + 25x - 70 = 0 \] 4. **Now we can solve the quadratic equation** using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\): Here \(a = 4\), \(b = 25\), and \(c = -70\). \[ x = \frac{-25 \pm \sqrt{25^2 - 4 \cdot 4 \cdot (-70)}}{2 \cdot 4} \] \[ x = \frac{-25 \pm \sqrt{625 + 1120}}{8} \] \[ x = \frac{-25 \pm \sqrt{1745}}{8} \] 5. **Calculating the discriminant**: \(\sqrt{1745} \approx 41.8\) Thus: \[ x = \frac{-25 \pm 41.8}{8} \] 6. **Finding the two possible values for \(x\)**: 1. \( x = \frac{-25 + 41.8}{8} = \frac{16.8}{8} \approx 2.1\) 2. \( x = \frac{-25 - 41.8}{8} = \frac{-66.8}{8} \approx -8.35\) Therefore, the solutions are approximately: \[ x \approx 2.1 \quad \text{and} \quad x \approx -8.35 \] Make sure to clarify the notation if the angle operation or any other detail affects the calculation.