x(x-8)=18

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Solution for x(x-8)=18 equation:



x(x-8)=18
We move all terms to the left:
x(x-8)-(18)=0
We multiply parentheses
x^2-8x-18=0
a = 1; b = -8; c = -18;
Δ = b2-4ac
Δ = -82-4·1·(-18)
Δ = 136
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:
$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*1}=\frac{8-2\sqrt{34}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*1}=\frac{8+2\sqrt{34}}{2} $

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