15=6x+x(x-13)

Solution for 15=6x+x(x-13) equation:

15=6x+x(x-13)

We move all terms to the left:

15-(6x+x(x-13))=0


We calculate terms in parentheses: -(6x+x(x-13)), so:

6x+x(x-13)

We multiply parentheses

x^2+6x-13x

We add all the numbers together, and all the variables

x^2-7x

Back to the equation:

-(x^2-7x)


We get rid of parentheses

-x^2+7x+15=0

We add all the numbers together, and all the variables

-1x^2+7x+15=0

a = -1; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-1)·15
Δ = 109
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{109}}{2*-1}=\frac{-7-\sqrt{109}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{109}}{2*-1}=\frac{-7+\sqrt{109}}{-2}
$