4w^2-5w=6

Solution for 4w^2-5w=6 equation:

4w^2-5w=6

We move all terms to the left:

4w^2-5w-(6)=0

a = 4; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·4·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*4}=\frac{-6}{8}
=-3/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*4}=\frac{16}{8}
=2
$