3/18x=7-18x

Solution for 3/18x=7-18x equation:

3/18x=7-18x

We move all terms to the left:

3/18x-(7-18x)=0


Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R


We add all the numbers together, and all the variables

3/18x-(-18x+7)=0

We get rid of parentheses

3/18x+18x-7=0

We multiply all the terms by the denominator


18x*18x-7*18x+3=0

Wy multiply elements

324x^2-126x+3=0

a = 324; b = -126; c = +3;
Δ = b2-4ac
Δ = -1262-4·324·3
Δ = 11988
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:

$\sqrt{\Delta}=\sqrt{11988}=\sqrt{324*37}=\sqrt{324}*\sqrt{37}=18\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-18\sqrt{37}}{2*324}=\frac{126-18\sqrt{37}}{648}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+18\sqrt{37}}{2*324}=\frac{126+18\sqrt{37}}{648}
$