37w-11=-4/7w

Solution for 37w-11=-4/7w equation:

37w-11=-4/7w

We move all terms to the left:

37w-11-(-4/7w)=0


Domain of the equation: 7w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

37w+4/7w-11=0

We multiply all the terms by the denominator


37w*7w-11*7w+4=0

Wy multiply elements

259w^2-77w+4=0

a = 259; b = -77; c = +4;
Δ = b2-4ac
Δ = -772-4·259·4
Δ = 1785
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{-(-77)-\sqrt{1785}}{2*259}=\frac{77-\sqrt{1785}}{518}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+\sqrt{1785}}{2*259}=\frac{77+\sqrt{1785}}{518}
$