56w^2+w=1

Solution for 56w^2+w=1 equation:

56w^2+w=1

We move all terms to the left:

56w^2+w-(1)=0

a = 56; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·56·(-1)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*56}=\frac{-16}{112}
=-1/7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*56}=\frac{14}{112}
=1/8
$