4w^2+3w=46

Solution for 4w^2+3w=46 equation:

4w^2+3w=46

We move all terms to the left:

4w^2+3w-(46)=0

a = 4; b = 3; c = -46;
Δ = b2-4ac
Δ = 32-4·4·(-46)
Δ = 745
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{745}}{2*4}=\frac{-3-\sqrt{745}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{745}}{2*4}=\frac{-3+\sqrt{745}}{8}
$