2x^2=11x+1

Solution for 2x^2=11x+1 equation:

2x^2=11x+1

We move all terms to the left:

2x^2-(11x+1)=0

We get rid of parentheses

2x^2-11x-1=0

a = 2; b = -11; c = -1;
Δ = b2-4ac
Δ = -112-4·2·(-1)
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*2}=\frac{11-\sqrt{129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{129}}{2*2}=\frac{11+\sqrt{129}}{4}
$