w^2+2w+1=2w^2-5w+11

Solution for w^2+2w+1=2w^2-5w+11 equation:

w^2+2w+1=2w^2-5w+11

We move all terms to the left:

w^2+2w+1-(2w^2-5w+11)=0

We get rid of parentheses

w^2-2w^2+2w+5w-11+1=0

We add all the numbers together, and all the variables

-1w^2+7w-10=0

a = -1; b = 7; c = -10;
Δ = b2-4ac
Δ = 72-4·(-1)·(-10)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3}{2*-1}=\frac{-10}{-2}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3}{2*-1}=\frac{-4}{-2}
=+2
$