4w^2-14w-48=0

Solution for 4w^2-14w-48=0 equation:

4w^2-14w-48=0

a = 4; b = -14; c = -48;
Δ = b2-4ac
Δ = -142-4·4·(-48)
Δ = 964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{241}}{2*4}=\frac{14-2\sqrt{241}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{241}}{2*4}=\frac{14+2\sqrt{241}}{8}
$