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5x(2x+110)=180
We move all terms to the left:
5x(2x+110)-(180)=0
We multiply parentheses
10x^2+550x-180=0
a = 10; b = 550; c = -180;
Δ = b2-4ac
Δ = 5502-4·10·(-180)
Δ = 309700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{309700}=\sqrt{100*3097}=\sqrt{100}*\sqrt{3097}=10\sqrt{3097}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(550)-10\sqrt{3097}}{2*10}=\frac{-550-10\sqrt{3097}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(550)+10\sqrt{3097}}{2*10}=\frac{-550+10\sqrt{3097}}{20} $
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