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5(x-36)-(x+36)-48-x(x-48)=0
We multiply parentheses
-x^2+5x-(x+36)+48x-180-48=0
We get rid of parentheses
-x^2+5x-x+48x-36-180-48=0
We add all the numbers together, and all the variables
-1x^2+52x-264=0
a = -1; b = 52; c = -264;
Δ = b2-4ac
Δ = 522-4·(-1)·(-264)
Δ = 1648
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1648}=\sqrt{16*103}=\sqrt{16}*\sqrt{103}=4\sqrt{103}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{103}}{2*-1}=\frac{-52-4\sqrt{103}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{103}}{2*-1}=\frac{-52+4\sqrt{103}}{-2} $
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