11-4x=2x^2-5

Solution for 11-4x=2x^2-5 equation:

11-4x=2x^2-5

We move all terms to the left:

11-4x-(2x^2-5)=0

We get rid of parentheses

-2x^2-4x+5+11=0

We add all the numbers together, and all the variables

-2x^2-4x+16=0

a = -2; b = -4; c = +16;
Δ = b2-4ac
Δ = -42-4·(-2)·16
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-12}{2*-2}=\frac{-8}{-4}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*-2}=\frac{16}{-4}
=-4
$