x*(x-10)=26

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Solution for x*(x-10)=26 equation:



x(x-10)=26
We move all terms to the left:
x(x-10)-(26)=0
We multiply parentheses
x^2-10x-26=0
a = 1; b = -10; c = -26;
Δ = b2-4ac
Δ = -102-4·1·(-26)
Δ = 204
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:
$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{51}}{2*1}=\frac{10-2\sqrt{51}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{51}}{2*1}=\frac{10+2\sqrt{51}}{2} $

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