x^2+3x-7=2x^2-7x-31

Solution for x^2+3x-7=2x^2-7x-31 equation:

x^2+3x-7=2x^2-7x-31

We move all terms to the left:

x^2+3x-7-(2x^2-7x-31)=0

We get rid of parentheses

x^2-2x^2+3x+7x+31-7=0

We add all the numbers together, and all the variables

-1x^2+10x+24=0

a = -1; b = 10; c = +24;
Δ = b2-4ac
Δ = 102-4·(-1)·24
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-1}=\frac{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-1}=\frac{4}{-2}
=-2
$