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(x-2)(x-5)=8

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Solution for (x-2)(x-5)=8 equation:



(x-2)(x-5)=8
We move all terms to the left:
(x-2)(x-5)-(8)=0
We multiply parentheses ..
(+x^2-5x-2x+10)-8=0
We get rid of parentheses
x^2-5x-2x+10-8=0
We add all the numbers together, and all the variables
x^2-7x+2=0
a = 1; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·1·2
Δ = 41
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{-(-7)-\sqrt{41}}{2*1}=\frac{7-\sqrt{41}}{2}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{41}}{2*1}=\frac{7+\sqrt{41}}{2}

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