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4x(x-5)=4x-5
We move all terms to the left:
4x(x-5)-(4x-5)=0
We multiply parentheses
4x^2-20x-(4x-5)=0
We get rid of parentheses
4x^2-20x-4x+5=0
We add all the numbers together, and all the variables
4x^2-24x+5=0
a = 4; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·4·5
Δ = 496
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{31}}{2*4}=\frac{24-4\sqrt{31}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{31}}{2*4}=\frac{24+4\sqrt{31}}{8} $
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