6w^2=25w+9

Solution for 6w^2=25w+9 equation:

6w^2=25w+9

We move all terms to the left:

6w^2-(25w+9)=0

We get rid of parentheses

6w^2-25w-9=0

a = 6; b = -25; c = -9;
Δ = b2-4ac
Δ = -252-4·6·(-9)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-29}{2*6}=\frac{-4}{12}
=-1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+29}{2*6}=\frac{54}{12}
=4+1/2
$