7w^2+2w-3=0

Solution for 7w^2+2w-3=0 equation:

7w^2+2w-3=0

a = 7; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·7·(-3)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{22}}{2*7}=\frac{-2-2\sqrt{22}}{14}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{22}}{2*7}=\frac{-2+2\sqrt{22}}{14}
$