1/2x+24=8x-4

Solution for 1/2x+24=8x-4 equation:

1/2x+24=8x-4

We move all terms to the left:

1/2x+24-(8x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-8x+4+24=0

We multiply all the terms by the denominator


-8x*2x+4*2x+24*2x+1=0

Wy multiply elements

-16x^2+8x+48x+1=0

We add all the numbers together, and all the variables

-16x^2+56x+1=0

a = -16; b = 56; c = +1;
Δ = b2-4ac
Δ = 562-4·(-16)·1
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-40\sqrt{2}}{2*-16}=\frac{-56-40\sqrt{2}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+40\sqrt{2}}{2*-16}=\frac{-56+40\sqrt{2}}{-32}
$