40w^2-108=-156w

Solution for 40w^2-108=-156w equation:

40w^2-108=-156w

We move all terms to the left:

40w^2-108-(-156w)=0

We get rid of parentheses

40w^2+156w-108=0

a = 40; b = 156; c = -108;
Δ = b2-4ac
Δ = 1562-4·40·(-108)
Δ = 41616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{41616}=204$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-204}{2*40}=\frac{-360}{80}
=-4+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+204}{2*40}=\frac{48}{80}
=3/5
$