w(10w+3)-7=0

Solution for w(10w+3)-7=0 equation:

w(10w+3)-7=0

We multiply parentheses

10w^2+3w-7=0

a = 10; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·10·(-7)
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{-(3)-17}{2*10}=\frac{-20}{20}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+17}{2*10}=\frac{14}{20}
=7/10
$