4w^2-6w-54=0

Solution for 4w^2-6w-54=0 equation:

4w^2-6w-54=0

a = 4; b = -6; c = -54;
Δ = b2-4ac
Δ = -62-4·4·(-54)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*4}=\frac{-24}{8}
=-3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*4}=\frac{36}{8}
=4+1/2
$