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(x-1)(x-5)=x+4x

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Solution for (x-1)(x-5)=x+4x equation:



(x-1)(x-5)=x+4x
We move all terms to the left:
(x-1)(x-5)-(x+4x)=0
We add all the numbers together, and all the variables
(x-1)(x-5)-(+5x)=0
We get rid of parentheses
(x-1)(x-5)-5x=0
We multiply parentheses ..
(+x^2-5x-1x+5)-5x=0
We get rid of parentheses
x^2-5x-1x-5x+5=0
We add all the numbers together, and all the variables
x^2-11x+5=0
a = 1; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·1·5
Δ = 101
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{-(-11)-\sqrt{101}}{2*1}=\frac{11-\sqrt{101}}{2}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{101}}{2*1}=\frac{11+\sqrt{101}}{2}

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