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 = 4012
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:

$\sqrt{\Delta}=\sqrt{4012}=\sqrt{4*1003}=\sqrt{4}*\sqrt{1003}=2\sqrt{1003}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{1003}}{2*9}=\frac{50-2\sqrt{1003}}{18}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{1003}}{2*9}=\frac{50+2\sqrt{1003}}{18}
$