4x+6=1/2x-1

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

4x+6=1/2x-1

We move all terms to the left:

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


Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

8x^2+2x+12x-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 = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{57}}{2*8}=\frac{-14-2\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{57}}{2*8}=\frac{-14+2\sqrt{57}}{16}
$