1/2x+1/2x=5x+1

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

1/2x+1/2x=5x+1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -10; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-10)·2
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{21}}{2*-10}=\frac{2-2\sqrt{21}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{21}}{2*-10}=\frac{2+2\sqrt{21}}{-20}
$