7w=4w^2+2

Solution for 7w=4w^2+2 equation:

7w=4w^2+2

We move all terms to the left:

7w-(4w^2+2)=0

We get rid of parentheses

-4w^2+7w-2=0

a = -4; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-4)·(-2)
Δ = 17
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{-(7)-\sqrt{17}}{2*-4}=\frac{-7-\sqrt{17}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*-4}=\frac{-7+\sqrt{17}}{-8}
$