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8x(3x-57)=1080
We move all terms to the left:
8x(3x-57)-(1080)=0
We multiply parentheses
24x^2-456x-1080=0
a = 24; b = -456; c = -1080;
Δ = b2-4ac
Δ = -4562-4·24·(-1080)
Δ = 311616
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{311616}=\sqrt{576*541}=\sqrt{576}*\sqrt{541}=24\sqrt{541}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-456)-24\sqrt{541}}{2*24}=\frac{456-24\sqrt{541}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-456)+24\sqrt{541}}{2*24}=\frac{456+24\sqrt{541}}{48} $
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