A=3x2+5x-6

Solution for A=3x2+5x-6 equation:

=3A^2+5A-6

We move all terms to the left:

-(3A^2+5A-6)=0

We get rid of parentheses

-3A^2-5A+6=0

a = -3; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-3)·6
Δ = 97
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{-(-5)-\sqrt{97}}{2*-3}=\frac{5-\sqrt{97}}{-6}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{97}}{2*-3}=\frac{5+\sqrt{97}}{-6}
$