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(6x-12)4x=180
We move all terms to the left:
(6x-12)4x-(180)=0
We multiply parentheses
24x^2-48x-180=0
a = 24; b = -48; c = -180;
Δ = b2-4ac
Δ = -482-4·24·(-180)
Δ = 19584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19584}=\sqrt{576*34}=\sqrt{576}*\sqrt{34}=24\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{34}}{2*24}=\frac{48-24\sqrt{34}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{34}}{2*24}=\frac{48+24\sqrt{34}}{48} $
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