w+12/3w=5=2/3

Solution for w+12/3w=5=2/3 equation:

w+12/3w=5=2/3

We move all terms to the left:

w+12/3w-(5)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We multiply all the terms by the denominator


w*3w-5*3w+12=0

Wy multiply elements

3w^2-15w+12=0

a = 3; b = -15; c = +12;
Δ = b2-4ac
Δ = -152-4·3·12
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*3}=\frac{6}{6}
=1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*3}=\frac{24}{6}
=4
$