4x-1=-1/2x+6

Solution for 4x-1=-1/2x+6 equation:

4x-1=-1/2x+6

We move all terms to the left:

4x-1-(-1/2x+6)=0


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

4x+1/2x-6-1=0

We multiply all the terms by the denominator


4x*2x-6*2x-1*2x+1=0

Wy multiply elements

8x^2-12x-2x+1=0

We add all the numbers together, and all the variables

8x^2-14x+1=0

a = 8; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·8·1
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{41}}{2*8}=\frac{14-2\sqrt{41}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{41}}{2*8}=\frac{14+2\sqrt{41}}{16}
$