15x(x+2)=6x(2x+7)

Solution for 15x(x+2)=6x(2x+7) equation:

15x(x+2)=6x(2x+7)

We move all terms to the left:

15x(x+2)-(6x(2x+7))=0

We multiply parentheses

15x^2+30x-(6x(2x+7))=0


We calculate terms in parentheses: -(6x(2x+7)), so:

6x(2x+7)

We multiply parentheses

12x^2+42x

Back to the equation:

-(12x^2+42x)


We get rid of parentheses

15x^2-12x^2+30x-42x=0

We add all the numbers together, and all the variables

3x^2-12x=0

a = 3; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·3·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*3}=\frac{24}{6}
=4
$