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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3A(2A+5)-(2A+5)), so:

3A(2A+5)-(2A+5)

We multiply parentheses

6A^2+15A-(2A+5)

We get rid of parentheses

6A^2+15A-2A-5

We add all the numbers together, and all the variables

6A^2+13A-5

Back to the equation:

-(6A^2+13A-5)


We get rid of parentheses

-6A^2-13A+5=0

a = -6; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·(-6)·5
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*-6}=\frac{-4}{-12}
=1/3
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*-6}=\frac{30}{-12}
=-2+1/2
$