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

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

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

We move all terms to the left:

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

We multiply parentheses

12x^2+30x-(2x(5x-3))=0


We calculate terms in parentheses: -(2x(5x-3)), so:

2x(5x-3)

We multiply parentheses

10x^2-6x

Back to the equation:

-(10x^2-6x)


We get rid of parentheses

12x^2-10x^2+30x+6x=0

We add all the numbers together, and all the variables

2x^2+36x=0

a = 2; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·2·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*2}=\frac{-72}{4}
=-18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*2}=\frac{0}{4}
=0
$