6w^2=19w+7

Solution for 6w^2=19w+7 equation:

6w^2=19w+7

We move all terms to the left:

6w^2-(19w+7)=0

We get rid of parentheses

6w^2-19w-7=0

a = 6; b = -19; c = -7;
Δ = b2-4ac
Δ = -192-4·6·(-7)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-23}{2*6}=\frac{-4}{12}
=-1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+23}{2*6}=\frac{42}{12}
=3+1/2
$