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2x^2+2x=80
We move all terms to the left:
2x^2+2x-(80)=0
a = 2; b = 2; c = -80;
Δ = b2-4ac
Δ = 22-4·2·(-80)
Δ = 644
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{644}=\sqrt{4*161}=\sqrt{4}*\sqrt{161}=2\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{161}}{2*2}=\frac{-2-2\sqrt{161}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{161}}{2*2}=\frac{-2+2\sqrt{161}}{4} $
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