x2-11x+3=5

Solution for x2-11x+3=5 equation:

x2-11x+3=5

We move all terms to the left:

x2-11x+3-(5)=0

We add all the numbers together, and all the variables

x^2-11x-2=0

a = 1; b = -11; c = -2;
Δ = b2-4ac
Δ = -112-4·1·(-2)
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{129}}{2*1}=\frac{11-\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{129}}{2*1}=\frac{11+\sqrt{129}}{2}
$