6(3w+4)=10w(2w-1)

Solution for 6(3w+4)=10w(2w-1) equation:

6(3w+4)=10w(2w-1)

We move all terms to the left:

6(3w+4)-(10w(2w-1))=0

We multiply parentheses

18w-(10w(2w-1))+24=0


We calculate terms in parentheses: -(10w(2w-1)), so:

10w(2w-1)

We multiply parentheses

20w^2-10w

Back to the equation:

-(20w^2-10w)


We get rid of parentheses

-20w^2+18w+10w+24=0

We add all the numbers together, and all the variables

-20w^2+28w+24=0

a = -20; b = 28; c = +24;
Δ = b2-4ac
Δ = 282-4·(-20)·24
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-52}{2*-20}=\frac{-80}{-40}
=+2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+52}{2*-20}=\frac{24}{-40}
=-3/5
$