-98+14w^2=189w

Solution for -98+14w^2=189w equation:

-98+14w^2=189w

We move all terms to the left:

-98+14w^2-(189w)=0

a = 14; b = -189; c = -98;
Δ = b2-4ac
Δ = -1892-4·14·(-98)
Δ = 41209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41209}=203$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-203}{2*14}=\frac{-14}{28}
=-1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+203}{2*14}=\frac{392}{28}
=14
$