(3w-1)(4w-2)=-11w+3

Solution for (3w-1)(4w-2)=-11w+3 equation:

(3w-1)(4w-2)=-11w+3

We move all terms to the left:

(3w-1)(4w-2)-(-11w+3)=0

We get rid of parentheses

(3w-1)(4w-2)+11w-3=0

We multiply parentheses ..

(+12w^2-6w-4w+2)+11w-3=0

We get rid of parentheses

12w^2-6w-4w+11w+2-3=0

We add all the numbers together, and all the variables

12w^2+w-1=0

a = 12; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·12·(-1)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*12}=\frac{-8}{24}
=-1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*12}=\frac{6}{24}
=1/4
$