4/3w+3=w+5

Solution for 4/3w+3=w+5 equation:

4/3w+3=w+5

We move all terms to the left:

4/3w+3-(w+5)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We get rid of parentheses

4/3w-w-5+3=0

We multiply all the terms by the denominator


-w*3w-5*3w+3*3w+4=0

Wy multiply elements

-3w^2-15w+9w+4=0

We add all the numbers together, and all the variables

-3w^2-6w+4=0

a = -3; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·(-3)·4
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*-3}=\frac{6-2\sqrt{21}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*-3}=\frac{6+2\sqrt{21}}{-6}
$