2(4w-1)=-10w(w-3)+4

Solution for 2(4w-1)=-10w(w-3)+4 equation:

2(4w-1)=-10w(w-3)+4

We move all terms to the left:

2(4w-1)-(-10w(w-3)+4)=0

We multiply parentheses

8w-(-10w(w-3)+4)-2=0


We calculate terms in parentheses: -(-10w(w-3)+4), so:

-10w(w-3)+4

We multiply parentheses

-10w^2+30w+4

Back to the equation:

-(-10w^2+30w+4)


We get rid of parentheses

10w^2-30w+8w-4-2=0

We add all the numbers together, and all the variables

10w^2-22w-6=0

a = 10; b = -22; c = -6;
Δ = b2-4ac
Δ = -222-4·10·(-6)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{181}}{2*10}=\frac{22-2\sqrt{181}}{20}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{181}}{2*10}=\frac{22+2\sqrt{181}}{20}
$