6x+48/18x+18=5

Solution for 6x+48/18x+18=5 equation:

6x+48/18x+18=5

We move all terms to the left:

6x+48/18x+18-(5)=0


Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R


We add all the numbers together, and all the variables

6x+48/18x+13=0

We multiply all the terms by the denominator


6x*18x+13*18x+48=0

Wy multiply elements

108x^2+234x+48=0

a = 108; b = 234; c = +48;
Δ = b2-4ac
Δ = 2342-4·108·48
Δ = 34020
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:

$\sqrt{\Delta}=\sqrt{34020}=\sqrt{324*105}=\sqrt{324}*\sqrt{105}=18\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(234)-18\sqrt{105}}{2*108}=\frac{-234-18\sqrt{105}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(234)+18\sqrt{105}}{2*108}=\frac{-234+18\sqrt{105}}{216}
$