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6x(4x+20)=180
We move all terms to the left:
6x(4x+20)-(180)=0
We multiply parentheses
24x^2+120x-180=0
a = 24; b = 120; c = -180;
Δ = b2-4ac
Δ = 1202-4·24·(-180)
Δ = 31680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31680}=\sqrt{576*55}=\sqrt{576}*\sqrt{55}=24\sqrt{55}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{55}}{2*24}=\frac{-120-24\sqrt{55}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{55}}{2*24}=\frac{-120+24\sqrt{55}}{48} $
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