2w^2+5w+2=3(2w+1)

Solution for 2w^2+5w+2=3(2w+1) equation:

2w^2+5w+2=3(2w+1)

We move all terms to the left:

2w^2+5w+2-(3(2w+1))=0


We calculate terms in parentheses: -(3(2w+1)), so:

3(2w+1)

We multiply parentheses

6w+3

Back to the equation:

-(6w+3)


We get rid of parentheses

2w^2+5w-6w-3+2=0

We add all the numbers together, and all the variables

2w^2-1w-1=0

a = 2; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·2·(-1)
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{-(-1)-3}{2*2}=\frac{-2}{4}
=-1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*2}=\frac{4}{4}
=1
$