5x^2-7x+5-(-7x^2-9x+12)=0

Solution for 5x^2-7x+5-(-7x^2-9x+12)=0 equation:

5x^2-7x+5-(-7x^2-9x+12)=0

We get rid of parentheses

5x^2+7x^2+9x-7x-12+5=0

We add all the numbers together, and all the variables

12x^2+2x-7=0

a = 12; b = 2; c = -7;
Δ = b2-4ac
Δ = 22-4·12·(-7)
Δ = 340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{85}}{2*12}=\frac{-2-2\sqrt{85}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{85}}{2*12}=\frac{-2+2\sqrt{85}}{24}
$