9w^2-50w+42=0

Solution for 9w^2-50w+42=0 equation:

9w^2-50w+42=0

a = 9; b = -50; c = +42;
Δ = b2-4ac
Δ = -502-4·9·42
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{247}}{2*9}=\frac{50-2\sqrt{247}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{247}}{2*9}=\frac{50+2\sqrt{247}}{18}
$