5x+1=1/2x+12

Solution for 5x+1=1/2x+12 equation:

5x+1=1/2x+12

We move all terms to the left:

5x+1-(1/2x+12)=0


Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

5x-1/2x-12+1=0

We multiply all the terms by the denominator


5x*2x-12*2x+1*2x-1=0

Wy multiply elements

10x^2-24x+2x-1=0

We add all the numbers together, and all the variables

10x^2-22x-1=0

a = 10; b = -22; c = -1;
Δ = b2-4ac
Δ = -222-4·10·(-1)
Δ = 524
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:

$\sqrt{\Delta}=\sqrt{524}=\sqrt{4*131}=\sqrt{4}*\sqrt{131}=2\sqrt{131}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{131}}{2*10}=\frac{22-2\sqrt{131}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{131}}{2*10}=\frac{22+2\sqrt{131}}{20}
$