5x-1=1/2x+18

Solution for 5x-1=1/2x+18 equation:

5x-1=1/2x+18

We move all terms to the left:

5x-1-(1/2x+18)=0


Domain of the equation: 2x+18)!=0

x∈R


We get rid of parentheses

5x-1/2x-18-1=0

We multiply all the terms by the denominator


5x*2x-18*2x-1*2x-1=0

Wy multiply elements

10x^2-36x-2x-1=0

We add all the numbers together, and all the variables

10x^2-38x-1=0

a = 10; b = -38; c = -1;
Δ = b2-4ac
Δ = -382-4·10·(-1)
Δ = 1484
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:

$\sqrt{\Delta}=\sqrt{1484}=\sqrt{4*371}=\sqrt{4}*\sqrt{371}=2\sqrt{371}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{371}}{2*10}=\frac{38-2\sqrt{371}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{371}}{2*10}=\frac{38+2\sqrt{371}}{20}
$