4.w^2+3w=3

Solution for 4.w^2+3w=3 equation:

4.w^2+3w=3

We move all terms to the left:

4.w^2+3w-(3)=0

a = 4.; b = 3; c = -3;
Δ = b2-4ac
Δ = 32-4·4.·(-3)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{57}}{2*4.}=\frac{-3-\sqrt{57}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*4.}=\frac{-3+\sqrt{57}}{8}
$