180-24x-30x+4x^2=88

Solution for 180-24x-30x+4x^2=88 equation:

180-24x-30x+4x^2=88

We move all terms to the left:

180-24x-30x+4x^2-(88)=0

We add all the numbers together, and all the variables

4x^2-54x+92=0

a = 4; b = -54; c = +92;
Δ = b2-4ac
Δ = -542-4·4·92
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-38}{2*4}=\frac{16}{8}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+38}{2*4}=\frac{92}{8}
=11+1/2
$