55/6x+3=20-5x

Solution for 55/6x+3=20-5x equation:

55/6x+3=20-5x

We move all terms to the left:

55/6x+3-(20-5x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

55/6x-(-5x+20)+3=0

We get rid of parentheses

55/6x+5x-20+3=0

We multiply all the terms by the denominator


5x*6x-20*6x+3*6x+55=0

Wy multiply elements

30x^2-120x+18x+55=0

We add all the numbers together, and all the variables

30x^2-102x+55=0

a = 30; b = -102; c = +55;
Δ = b2-4ac
Δ = -1022-4·30·55
Δ = 3804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3804}=\sqrt{4*951}=\sqrt{4}*\sqrt{951}=2\sqrt{951}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{951}}{2*30}=\frac{102-2\sqrt{951}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{951}}{2*30}=\frac{102+2\sqrt{951}}{60}
$