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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-(3(+2x^2+5x-10x-25))=0


We calculate terms in parentheses: -(3(+2x^2+5x-10x-25)), so:

3(+2x^2+5x-10x-25)

We multiply parentheses

6x^2+15x-30x-75

We add all the numbers together, and all the variables

6x^2-15x-75

Back to the equation:

-(6x^2-15x-75)


We get rid of parentheses

-6x^2+15x+75=0

a = -6; b = 15; c = +75;
Δ = b2-4ac
Δ = 152-4·(-6)·75
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-45}{2*-6}=\frac{-60}{-12}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+45}{2*-6}=\frac{30}{-12}
=-2+1/2
$