2x=x2+5x-11

Solution for 2x=x2+5x-11 equation:

2x=x2+5x-11

We move all terms to the left:

2x-(x2+5x-11)=0

We add all the numbers together, and all the variables

-(+x^2+5x-11)+2x=0

We get rid of parentheses

-x^2-5x+2x+11=0

We add all the numbers together, and all the variables

-1x^2-3x+11=0

a = -1; b = -3; c = +11;
Δ = b2-4ac
Δ = -32-4·(-1)·11
Δ = 53
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{-(-3)-\sqrt{53}}{2*-1}=\frac{3-\sqrt{53}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{53}}{2*-1}=\frac{3+\sqrt{53}}{-2}
$