10w^2=19w+5

Solution for 10w^2=19w+5 equation:

10w^2=19w+5

We move all terms to the left:

10w^2-(19w+5)=0

We get rid of parentheses

10w^2-19w-5=0

a = 10; b = -19; c = -5;
Δ = b2-4ac
Δ = -192-4·10·(-5)
Δ = 561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{561}}{2*10}=\frac{19-\sqrt{561}}{20}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{561}}{2*10}=\frac{19+\sqrt{561}}{20}
$