(2x^2+7x-12)-(x^2-16)=0

Solution for (2x^2+7x-12)-(x^2-16)=0 equation:

(2x^2+7x-12)-(x^2-16)=0

We get rid of parentheses

2x^2-x^2+7x-12+16=0

We add all the numbers together, and all the variables

x^2+7x+4=0

a = 1; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·1·4
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{33}}{2*1}=\frac{-7-\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{33}}{2*1}=\frac{-7+\sqrt{33}}{2}
$