4w^2+26w-56=0

Solution for 4w^2+26w-56=0 equation:

4w^2+26w-56=0

a = 4; b = 26; c = -56;
Δ = b2-4ac
Δ = 262-4·4·(-56)
Δ = 1572
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:

$\sqrt{\Delta}=\sqrt{1572}=\sqrt{4*393}=\sqrt{4}*\sqrt{393}=2\sqrt{393}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{393}}{2*4}=\frac{-26-2\sqrt{393}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{393}}{2*4}=\frac{-26+2\sqrt{393}}{8}
$