x^2+10x-6=9

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Solution for x^2+10x-6=9 equation:



x^2+10x-6=9
We move all terms to the left:
x^2+10x-6-(9)=0
We add all the numbers together, and all the variables
x^2+10x-15=0
a = 1; b = 10; c = -15;
Δ = b2-4ac
Δ = 102-4·1·(-15)
Δ = 160
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:
$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{10}}{2*1}=\frac{-10-4\sqrt{10}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{10}}{2*1}=\frac{-10+4\sqrt{10}}{2} $

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