0=6(2x+5)(5x-3)

Solution for 0=6(2x+5)(5x-3) equation:

0=6(2x+5)(5x-3)

We move all terms to the left:

0-(6(2x+5)(5x-3))=0

We add all the numbers together, and all the variables

-(6(2x+5)(5x-3))=0

We multiply parentheses ..

-(6(+10x^2-6x+25x-15))=0


We calculate terms in parentheses: -(6(+10x^2-6x+25x-15)), so:

6(+10x^2-6x+25x-15)

We multiply parentheses

60x^2-36x+150x-90

We add all the numbers together, and all the variables

60x^2+114x-90

Back to the equation:

-(60x^2+114x-90)


We get rid of parentheses

-60x^2-114x+90=0

a = -60; b = -114; c = +90;
Δ = b2-4ac
Δ = -1142-4·(-60)·90
Δ = 34596
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34596}=186$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-186}{2*-60}=\frac{-72}{-120}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+186}{2*-60}=\frac{300}{-120}
=-2+1/2
$