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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(2(+2x^2-3x-10x+15)), so:

2(+2x^2-3x-10x+15)

We multiply parentheses

4x^2-6x-20x+30

We add all the numbers together, and all the variables

4x^2-26x+30

Back to the equation:

-(4x^2-26x+30)


We get rid of parentheses

-4x^2+26x-30=0

a = -4; b = 26; c = -30;
Δ = b2-4ac
Δ = 262-4·(-4)·(-30)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-14}{2*-4}=\frac{-40}{-8}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+14}{2*-4}=\frac{-12}{-8}
=1+1/2
$