(3+5x)(2-3x)=12-15^2

Solution for (3+5x)(2-3x)=12-15^2 equation:

(3+5x)(2-3x)=12-15^2

We move all terms to the left:

(3+5x)(2-3x)-(12-15^2)=0

We add all the numbers together, and all the variables

(5x+3)(-3x+2)-(12-15^2)=0

We add all the numbers together, and all the variables

(5x+3)(-3x+2)+213=0

We multiply parentheses ..

(-15x^2+10x-9x+6)+213=0

We get rid of parentheses

-15x^2+10x-9x+6+213=0

We add all the numbers together, and all the variables

-15x^2+x+219=0

a = -15; b = 1; c = +219;
Δ = b2-4ac
Δ = 12-4·(-15)·219
Δ = 13141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{13141}}{2*-15}=\frac{-1-\sqrt{13141}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13141}}{2*-15}=\frac{-1+\sqrt{13141}}{-30}
$