10w2=7w+6

Solution for 10w2=7w+6 equation:

10w^2=7w+6

We move all terms to the left:

10w^2-(7w+6)=0

We get rid of parentheses

10w^2-7w-6=0

a = 10; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·10·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*10}=\frac{-10}{20}
=-1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*10}=\frac{24}{20}
=1+1/5
$