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8x+2x(5x-10)=110
We move all terms to the left:
8x+2x(5x-10)-(110)=0
We multiply parentheses
10x^2+8x-20x-110=0
We add all the numbers together, and all the variables
10x^2-12x-110=0
a = 10; b = -12; c = -110;
Δ = b2-4ac
Δ = -122-4·10·(-110)
Δ = 4544
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4544}=\sqrt{64*71}=\sqrt{64}*\sqrt{71}=8\sqrt{71}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{71}}{2*10}=\frac{12-8\sqrt{71}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{71}}{2*10}=\frac{12+8\sqrt{71}}{20} $
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