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(6x+32)4x=180
We move all terms to the left:
(6x+32)4x-(180)=0
We multiply parentheses
24x^2+128x-180=0
a = 24; b = 128; c = -180;
Δ = b2-4ac
Δ = 1282-4·24·(-180)
Δ = 33664
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{33664}=\sqrt{64*526}=\sqrt{64}*\sqrt{526}=8\sqrt{526}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-8\sqrt{526}}{2*24}=\frac{-128-8\sqrt{526}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+8\sqrt{526}}{2*24}=\frac{-128+8\sqrt{526}}{48} $
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