(x+10)x=10

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Solution for (x+10)x=10 equation:



(x+10)x=10
We move all terms to the left:
(x+10)x-(10)=0
We multiply parentheses
x^2+10x-10=0
a = 1; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·1·(-10)
Δ = 140
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:
$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{35}}{2*1}=\frac{-10-2\sqrt{35}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{35}}{2*1}=\frac{-10+2\sqrt{35}}{2} $

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