(9x^2-7x+5)-(12x^2-5x-6)=

Solution for (9x^2-7x+5)-(12x^2-5x-6)= equation:

(9x^2-7x+5)-(12x^2-5x-6)=

We move all terms to the left:

(9x^2-7x+5)-(12x^2-5x-6)-()=0

We add all the numbers together, and all the variables

(9x^2-7x+5)-(12x^2-5x-6)=0

We get rid of parentheses

9x^2-12x^2-7x+5x+5+6=0

We add all the numbers together, and all the variables

-3x^2-2x+11=0

a = -3; b = -2; c = +11;
Δ = b2-4ac
Δ = -22-4·(-3)·11
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{34}}{2*-3}=\frac{2-2\sqrt{34}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{34}}{2*-3}=\frac{2+2\sqrt{34}}{-6}
$