X^2+10x+x^2+34=135

Solution for X^2+10x+x^2+34=135 equation:

X^2+10X+X^2+34=135

We move all terms to the left:

X^2+10X+X^2+34-(135)=0

We add all the numbers together, and all the variables

2X^2+10X-101=0

a = 2; b = 10; c = -101;
Δ = b2-4ac
Δ = 102-4·2·(-101)
Δ = 908
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:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{227}}{2*2}=\frac{-10-2\sqrt{227}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{227}}{2*2}=\frac{-10+2\sqrt{227}}{4}
$