15x+x(x-1)=2(18+7x)

Solution for 15x+x(x-1)=2(18+7x) equation:

15x+x(x-1)=2(18+7x)

We move all terms to the left:

15x+x(x-1)-(2(18+7x))=0

We add all the numbers together, and all the variables

15x+x(x-1)-(2(7x+18))=0

We multiply parentheses

x^2+15x-1x-(2(7x+18))=0


We calculate terms in parentheses: -(2(7x+18)), so:

2(7x+18)

We multiply parentheses

14x+36

Back to the equation:

-(14x+36)


We add all the numbers together, and all the variables

x^2+14x-(14x+36)=0

We get rid of parentheses

x^2+14x-14x-36=0

We add all the numbers together, and all the variables

x^2-36=0

a = 1; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·1·(-36)
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{-(0)-12}{2*1}=\frac{-12}{2}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*1}=\frac{12}{2}
=6
$