5w2+6w-7=0

Solution for 5w2+6w-7=0 equation:

5w^2+6w-7=0

a = 5; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·5·(-7)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{11}}{2*5}=\frac{-6-4\sqrt{11}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{11}}{2*5}=\frac{-6+4\sqrt{11}}{10}
$