solve for x in the equation 2x² + 3x - 7 = x² + 5x + 39.\no x=-6±√82\no x=-6±2√17\no x=1±√33\no x=1±√47

Explanation:

Step1: Rearrange the equation

First, move all terms to one - side to get a quadratic equation in standard form $ax^{2}+bx + c = 0$. [ \begin{align*} 2x^{2}+3x - 7-(x^{2}+5x + 39)&=0\ 2x^{2}+3x - 7 - x^{2}-5x - 39&=0\ (2x^{2}-x^{2})+(3x - 5x)+(-7 - 39)&=0\ x^{2}-2x - 46&=0 \end{align*} ]

Step2: Apply the quadratic formula

The quadratic formula for a quadratic equation $ax^{2}+bx + c = 0$ is $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. For the equation $x^{2}-2x - 46 = 0$, we have $a = 1$, $b=-2$, and $c=-46$. [ \begin{align*} x&=\frac{-(-2)\pm\sqrt{(-2)^{2}-4\times1\times(-46)}}{2\times1}\ &=\frac{2\pm\sqrt{4 + 184}}{2}\ &=\frac{2\pm\sqrt{188}}{2}\ &=\frac{2\pm2\sqrt{47}}{2}\ &=1\pm\sqrt{47} \end{align*} ]

Answer:

$x = 1\pm\sqrt{47}$