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2x(48+2x)=180
We move all terms to the left:
2x(48+2x)-(180)=0
We add all the numbers together, and all the variables
2x(2x+48)-180=0
We multiply parentheses
4x^2+96x-180=0
a = 4; b = 96; c = -180;
Δ = b2-4ac
Δ = 962-4·4·(-180)
Δ = 12096
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-24\sqrt{21}}{2*4}=\frac{-96-24\sqrt{21}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+24\sqrt{21}}{2*4}=\frac{-96+24\sqrt{21}}{8} $
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