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

Solution for 5(x-3)(2x+5)=0 equation:

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

We multiply parentheses ..

5(+2x^2+5x-6x-15)=0

We multiply parentheses

10x^2+25x-30x-75=0

We add all the numbers together, and all the variables

10x^2-5x-75=0

a = 10; b = -5; c = -75;
Δ = b2-4ac
Δ = -52-4·10·(-75)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-55}{2*10}=\frac{-50}{20}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+55}{2*10}=\frac{60}{20}
=3
$