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5x(8x+63)=180
We move all terms to the left:
5x(8x+63)-(180)=0
We multiply parentheses
40x^2+315x-180=0
a = 40; b = 315; c = -180;
Δ = b2-4ac
Δ = 3152-4·40·(-180)
Δ = 128025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{128025}=\sqrt{225*569}=\sqrt{225}*\sqrt{569}=15\sqrt{569}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-15\sqrt{569}}{2*40}=\frac{-315-15\sqrt{569}}{80} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+15\sqrt{569}}{2*40}=\frac{-315+15\sqrt{569}}{80} $
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