37/w=5w-27

Solution for 37/w=5w-27 equation:

37/w=5w-27

We move all terms to the left:

37/w-(5w-27)=0


Domain of the equation: w!=0

w∈R


We get rid of parentheses

37/w-5w+27=0

We multiply all the terms by the denominator


-5w*w+27*w+37=0

We add all the numbers together, and all the variables

27w-5w*w+37=0

Wy multiply elements

-5w^2+27w+37=0

a = -5; b = 27; c = +37;
Δ = b2-4ac
Δ = 272-4·(-5)·37
Δ = 1469
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{-(27)-\sqrt{1469}}{2*-5}=\frac{-27-\sqrt{1469}}{-10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{1469}}{2*-5}=\frac{-27+\sqrt{1469}}{-10}
$