11w=4w^2-3

Solution for 11w=4w^2-3 equation:

11w=4w^2-3

We move all terms to the left:

11w-(4w^2-3)=0

We get rid of parentheses

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

a = -4; b = 11; c = +3;
Δ = b2-4ac
Δ = 112-4·(-4)·3
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*-4}=\frac{-24}{-8}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*-4}=\frac{2}{-8}
=-1/4
$