18-x(x-4)=-88

Solution for 18-x(x-4)=-88 equation:

18-x(x-4)=-88

We move all terms to the left:

18-x(x-4)-(-88)=0

We add all the numbers together, and all the variables

-x(x-4)+106=0

We multiply parentheses

-x^2+4x+106=0

We add all the numbers together, and all the variables

-1x^2+4x+106=0

a = -1; b = 4; c = +106;
Δ = b2-4ac
Δ = 42-4·(-1)·106
Δ = 440
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:

$\sqrt{\Delta}=\sqrt{440}=\sqrt{4*110}=\sqrt{4}*\sqrt{110}=2\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{110}}{2*-1}=\frac{-4-2\sqrt{110}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{110}}{2*-1}=\frac{-4+2\sqrt{110}}{-2}
$