x^2-13/2=x+11

Solution for x^2-13/2=x+11 equation:

x^2-13/2=x+11

We move all terms to the left:

x^2-13/2-(x+11)=0

We get rid of parentheses

x^2-x-11-13/2=0

We multiply all the terms by the denominator


x^2*2-x*2-13-11*2=0

We add all the numbers together, and all the variables

x^2*2-x*2-35=0

Wy multiply elements

2x^2-2x-35=0

a = 2; b = -2; c = -35;
Δ = b2-4ac
Δ = -22-4·2·(-35)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{71}}{2*2}=\frac{2-2\sqrt{71}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{71}}{2*2}=\frac{2+2\sqrt{71}}{4}
$