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(x-20)(4x-3)=180
We move all terms to the left:
(x-20)(4x-3)-(180)=0
We multiply parentheses ..
(+4x^2-3x-80x+60)-180=0
We get rid of parentheses
4x^2-3x-80x+60-180=0
We add all the numbers together, and all the variables
4x^2-83x-120=0
a = 4; b = -83; c = -120;
Δ = b2-4ac
Δ = -832-4·4·(-120)
Δ = 8809
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-\sqrt{8809}}{2*4}=\frac{83-\sqrt{8809}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+\sqrt{8809}}{2*4}=\frac{83+\sqrt{8809}}{8} $
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