(5a^2+6a+2)-(7a^2-7a+5)=0

Solution for (5a^2+6a+2)-(7a^2-7a+5)=0 equation:

(5a^2+6a+2)-(7a^2-7a+5)=0

We get rid of parentheses

5a^2-7a^2+6a+7a+2-5=0

We add all the numbers together, and all the variables

-2a^2+13a-3=0

a = -2; b = 13; c = -3;
Δ = b2-4ac
Δ = 132-4·(-2)·(-3)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-\sqrt{145}}{2*-2}=\frac{-13-\sqrt{145}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{145}}{2*-2}=\frac{-13+\sqrt{145}}{-4}
$