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(4x+16)6x=180
We move all terms to the left:
(4x+16)6x-(180)=0
We multiply parentheses
24x^2+96x-180=0
a = 24; b = 96; c = -180;
Δ = b2-4ac
Δ = 962-4·24·(-180)
Δ = 26496
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{26496}=\sqrt{576*46}=\sqrt{576}*\sqrt{46}=24\sqrt{46}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-24\sqrt{46}}{2*24}=\frac{-96-24\sqrt{46}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+24\sqrt{46}}{2*24}=\frac{-96+24\sqrt{46}}{48} $
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