x^2+12x=10=0

Solution for x^2+12x=10=0 equation:

x^2+12x=10=0

We move all terms to the left:

x^2+12x-(10)=0

a = 1; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·1·(-10)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{46}}{2*1}=\frac{-12-2\sqrt{46}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{46}}{2*1}=\frac{-12+2\sqrt{46}}{2}
$