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(2x-20)4x+20=180
We move all terms to the left:
(2x-20)4x+20-(180)=0
We add all the numbers together, and all the variables
(2x-20)4x-160=0
We multiply parentheses
8x^2-80x-160=0
a = 8; b = -80; c = -160;
Δ = b2-4ac
Δ = -802-4·8·(-160)
Δ = 11520
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11520}=\sqrt{2304*5}=\sqrt{2304}*\sqrt{5}=48\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-48\sqrt{5}}{2*8}=\frac{80-48\sqrt{5}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+48\sqrt{5}}{2*8}=\frac{80+48\sqrt{5}}{16} $
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