8x-2=1/212x+24

Solution for 8x-2=1/212x+24 equation:

8x-2=1/212x+24

We move all terms to the left:

8x-2-(1/212x+24)=0


Domain of the equation: 212x+24)!=0

x∈R


We get rid of parentheses

8x-1/212x-24-2=0

We multiply all the terms by the denominator


8x*212x-24*212x-2*212x-1=0

Wy multiply elements

1696x^2-5088x-424x-1=0

We add all the numbers together, and all the variables

1696x^2-5512x-1=0

a = 1696; b = -5512; c = -1;
Δ = b2-4ac
Δ = -55122-4·1696·(-1)
Δ = 30388928
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:

$\sqrt{\Delta}=\sqrt{30388928}=\sqrt{18496*1643}=\sqrt{18496}*\sqrt{1643}=136\sqrt{1643}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5512)-136\sqrt{1643}}{2*1696}=\frac{5512-136\sqrt{1643}}{3392}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5512)+136\sqrt{1643}}{2*1696}=\frac{5512+136\sqrt{1643}}{3392}
$