A=X(5x-4)+2x-6

Solution for A=X(5x-4)+2x-6 equation:

=A(5A-4)+2A-6

We move all terms to the left:

-(A(5A-4)+2A-6)=0


We calculate terms in parentheses: -(A(5A-4)+2A-6), so:

A(5A-4)+2A-6

We add all the numbers together, and all the variables

2A+A(5A-4)-6

We multiply parentheses

5A^2+2A-4A-6

We add all the numbers together, and all the variables

5A^2-2A-6

Back to the equation:

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


We get rid of parentheses

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

a = -5; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-5)·6
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{31}}{2*-5}=\frac{-2-2\sqrt{31}}{-10}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{31}}{2*-5}=\frac{-2+2\sqrt{31}}{-10}
$