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(12x-20)(4x/3)=180
We move all terms to the left:
(12x-20)(4x/3)-(180)=0
We add all the numbers together, and all the variables
(12x-20)(+4x/3)-180=0
We multiply parentheses ..
(+48x^2-80x)-180=0
We get rid of parentheses
48x^2-80x-180=0
a = 48; b = -80; c = -180;
Δ = b2-4ac
Δ = -802-4·48·(-180)
Δ = 40960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40960}=\sqrt{4096*10}=\sqrt{4096}*\sqrt{10}=64\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-64\sqrt{10}}{2*48}=\frac{80-64\sqrt{10}}{96} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+64\sqrt{10}}{2*48}=\frac{80+64\sqrt{10}}{96} $
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