X^2+11x+30.25=34

Solution for X^2+11x+30.25=34 equation:

X^2+11X+30.25=34

We move all terms to the left:

X^2+11X+30.25-(34)=0

We add all the numbers together, and all the variables

X^2+11X-3.75=0

a = 1; b = 11; c = -3.75;
Δ = b2-4ac
Δ = 112-4·1·(-3.75)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-2\sqrt{34}}{2*1}=\frac{-11-2\sqrt{34}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+2\sqrt{34}}{2*1}=\frac{-11+2\sqrt{34}}{2}
$