54+(-9x-5)(10-2x)=180

Solution for 54+(-9x-5)(10-2x)=180 equation:

54+(-9x-5)(10-2x)=180

We move all terms to the left:

54+(-9x-5)(10-2x)-(180)=0

We add all the numbers together, and all the variables

(-9x-5)(-2x+10)+54-180=0

We add all the numbers together, and all the variables

(-9x-5)(-2x+10)-126=0

We multiply parentheses ..

(+18x^2-90x+10x-50)-126=0

We get rid of parentheses

18x^2-90x+10x-50-126=0

We add all the numbers together, and all the variables

18x^2-80x-176=0

a = 18; b = -80; c = -176;
Δ = b2-4ac
Δ = -802-4·18·(-176)
Δ = 19072
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:

$\sqrt{\Delta}=\sqrt{19072}=\sqrt{64*298}=\sqrt{64}*\sqrt{298}=8\sqrt{298}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-8\sqrt{298}}{2*18}=\frac{80-8\sqrt{298}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+8\sqrt{298}}{2*18}=\frac{80+8\sqrt{298}}{36}
$