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4x(2x-6)=180
We move all terms to the left:
4x(2x-6)-(180)=0
We multiply parentheses
8x^2-24x-180=0
a = 8; b = -24; c = -180;
Δ = b2-4ac
Δ = -242-4·8·(-180)
Δ = 6336
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24\sqrt{11}}{2*8}=\frac{24-24\sqrt{11}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24\sqrt{11}}{2*8}=\frac{24+24\sqrt{11}}{16} $
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