5w^2-11=22-4w

Solution for 5w^2-11=22-4w equation:

5w^2-11=22-4w

We move all terms to the left:

5w^2-11-(22-4w)=0

We add all the numbers together, and all the variables

5w^2-(-4w+22)-11=0

We get rid of parentheses

5w^2+4w-22-11=0

We add all the numbers together, and all the variables

5w^2+4w-33=0

a = 5; b = 4; c = -33;
Δ = b2-4ac
Δ = 42-4·5·(-33)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-26}{2*5}=\frac{-30}{10}
=-3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+26}{2*5}=\frac{22}{10}
=2+1/5
$