(3+5x)(2-3x)=12115x^

Solution for (3+5x)(2-3x)=12115x^ equation:

(3+5x)(2-3x)=12115x^

We move all terms to the left:

(3+5x)(2-3x)-(12115x^)=0

We add all the numbers together, and all the variables

(5x+3)(-3x+2)-12115x^=0

We add all the numbers together, and all the variables

-12115x+(5x+3)(-3x+2)=0

We multiply parentheses ..

(-15x^2+10x-9x+6)-12115x=0

We get rid of parentheses

-15x^2+10x-9x-12115x+6=0

We add all the numbers together, and all the variables

-15x^2-12114x+6=0

a = -15; b = -12114; c = +6;
Δ = b2-4ac
Δ = -121142-4·(-15)·6
Δ = 146749356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{146749356}=\sqrt{36*4076371}=\sqrt{36}*\sqrt{4076371}=6\sqrt{4076371}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12114)-6\sqrt{4076371}}{2*-15}=\frac{12114-6\sqrt{4076371}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12114)+6\sqrt{4076371}}{2*-15}=\frac{12114+6\sqrt{4076371}}{-30}
$