-2x^2+11x-1=13

Solution for -2x^2+11x-1=13 equation:

-2x^2+11x-1=13

We move all terms to the left:

-2x^2+11x-1-(13)=0

We add all the numbers together, and all the variables

-2x^2+11x-14=0

a = -2; b = 11; c = -14;
Δ = b2-4ac
Δ = 112-4·(-2)·(-14)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3}{2*-2}=\frac{-8}{-4}
=+2
$