(x-15)(2x+1)=0

Solution for (x-15)(2x+1)=0 equation:

(x-15)(2x+1)=0

We multiply parentheses ..

(+2x^2+x-30x-15)=0

We get rid of parentheses

2x^2+x-30x-15=0

We add all the numbers together, and all the variables

2x^2-29x-15=0

a = 2; b = -29; c = -15;
Δ = b2-4ac
Δ = -292-4·2·(-15)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-31}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+31}{2*2}=\frac{60}{4}
=15
$