31/3w2-4=26

Solution for 31/3w2-4=26 equation:

31/3w^2-4=26

We move all terms to the left:

31/3w^2-4-(26)=0


Domain of the equation: 3w^2!=0

w^2!=0/3

w^2!=√0

w!=0

w∈R


We add all the numbers together, and all the variables

31/3w^2-30=0

We multiply all the terms by the denominator


-30*3w^2+31=0

Wy multiply elements

-90w^2+31=0

a = -90; b = 0; c = +31;
Δ = b2-4ac
Δ = 02-4·(-90)·31
Δ = 11160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11160}=\sqrt{36*310}=\sqrt{36}*\sqrt{310}=6\sqrt{310}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{310}}{2*-90}=\frac{0-6\sqrt{310}}{-180}
=-\frac{6\sqrt{310}}{-180}
=-\frac{\sqrt{310}}{-30}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{310}}{2*-90}=\frac{0+6\sqrt{310}}{-180}
=\frac{6\sqrt{310}}{-180}
=\frac{\sqrt{310}}{-30}
$