3w+4-w=5w(w-2)-2

Solution for 3w+4-w=5w(w-2)-2 equation:

3w+4-w=5w(w-2)-2

We move all terms to the left:

3w+4-w-(5w(w-2)-2)=0

We add all the numbers together, and all the variables

2w-(5w(w-2)-2)+4=0


We calculate terms in parentheses: -(5w(w-2)-2), so:

5w(w-2)-2

We multiply parentheses

5w^2-10w-2

Back to the equation:

-(5w^2-10w-2)


We get rid of parentheses

-5w^2+2w+10w+2+4=0

We add all the numbers together, and all the variables

-5w^2+12w+6=0

a = -5; b = 12; c = +6;
Δ = b2-4ac
Δ = 122-4·(-5)·6
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{66}}{2*-5}=\frac{-12-2\sqrt{66}}{-10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{66}}{2*-5}=\frac{-12+2\sqrt{66}}{-10}
$