A(x)=(5x-1)(3x-2)

Solution for A(x)=(5x-1)(3x-2) equation:

(A)=(5A-1)(3A-2)

We move all terms to the left:

(A)-((5A-1)(3A-2))=0

We multiply parentheses ..

-((+15A^2-10A-3A+2))+A=0


We calculate terms in parentheses: -((+15A^2-10A-3A+2)), so:

(+15A^2-10A-3A+2)

We get rid of parentheses

15A^2-10A-3A+2

We add all the numbers together, and all the variables

15A^2-13A+2

Back to the equation:

-(15A^2-13A+2)


We add all the numbers together, and all the variables

A-(15A^2-13A+2)=0

We get rid of parentheses

-15A^2+A+13A-2=0

We add all the numbers together, and all the variables

-15A^2+14A-2=0

a = -15; b = 14; c = -2;
Δ = b2-4ac
Δ = 142-4·(-15)·(-2)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{19}}{2*-15}=\frac{-14-2\sqrt{19}}{-30}
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{19}}{2*-15}=\frac{-14+2\sqrt{19}}{-30}
$