8x+4=1/2x-1

Solution for 8x+4=1/2x-1 equation:

8x+4=1/2x-1

We move all terms to the left:

8x+4-(1/2x-1)=0


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

x∈R


We get rid of parentheses

8x-1/2x+1+4=0

We multiply all the terms by the denominator


8x*2x+1*2x+4*2x-1=0

Wy multiply elements

16x^2+2x+8x-1=0

We add all the numbers together, and all the variables

16x^2+10x-1=0

a = 16; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·16·(-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{-(10)-2\sqrt{41}}{2*16}=\frac{-10-2\sqrt{41}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{41}}{2*16}=\frac{-10+2\sqrt{41}}{32}
$