15-x(x-4)=-68

Solution for 15-x(x-4)=-68 equation:

15-x(x-4)=-68

We move all terms to the left:

15-x(x-4)-(-68)=0

We add all the numbers together, and all the variables

-x(x-4)+83=0

We multiply parentheses

-x^2+4x+83=0

We add all the numbers together, and all the variables

-1x^2+4x+83=0

a = -1; b = 4; c = +83;
Δ = b2-4ac
Δ = 42-4·(-1)·83
Δ = 348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{87}}{2*-1}=\frac{-4-2\sqrt{87}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{87}}{2*-1}=\frac{-4+2\sqrt{87}}{-2}
$