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(5x)(9x-76)=180
We move all terms to the left:
(5x)(9x-76)-(180)=0
We multiply parentheses
45x^2-380x-180=0
a = 45; b = -380; c = -180;
Δ = b2-4ac
Δ = -3802-4·45·(-180)
Δ = 176800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{176800}=\sqrt{400*442}=\sqrt{400}*\sqrt{442}=20\sqrt{442}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-20\sqrt{442}}{2*45}=\frac{380-20\sqrt{442}}{90} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+20\sqrt{442}}{2*45}=\frac{380+20\sqrt{442}}{90} $
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