A(x)=6x^2-7x-5

Solution for A(x)=6x^2-7x-5 equation:

(A)=6A^2-7A-5

We move all terms to the left:

(A)-(6A^2-7A-5)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-6A^2+8A+5=0

a = -6; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-6)·5
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{46}}{2*-6}=\frac{-8-2\sqrt{46}}{-12}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{46}}{2*-6}=\frac{-8+2\sqrt{46}}{-12}
$