x^2+10x+5=134

Solution for x^2+10x+5=134 equation:

x^2+10x+5=134

We move all terms to the left:

x^2+10x+5-(134)=0

We add all the numbers together, and all the variables

x^2+10x-129=0

a = 1; b = 10; c = -129;
Δ = b2-4ac
Δ = 102-4·1·(-129)
Δ = 616
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:

$\sqrt{\Delta}=\sqrt{616}=\sqrt{4*154}=\sqrt{4}*\sqrt{154}=2\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{154}}{2*1}=\frac{-10-2\sqrt{154}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{154}}{2*1}=\frac{-10+2\sqrt{154}}{2}
$