(3x+10)(2x-15)=125

Solution for (3x+10)(2x-15)=125 equation:

(3x+10)(2x-15)=125

We move all terms to the left:

(3x+10)(2x-15)-(125)=0

We multiply parentheses ..

(+6x^2-45x+20x-150)-125=0

We get rid of parentheses

6x^2-45x+20x-150-125=0

We add all the numbers together, and all the variables

6x^2-25x-275=0

a = 6; b = -25; c = -275;
Δ = b2-4ac
Δ = -252-4·6·(-275)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-85}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+85}{2*6}=\frac{110}{12}
=9+1/6
$