24x-2=2/7x

Solution for 24x-2=2/7x equation:

24x-2=2/7x

We move all terms to the left:

24x-2-(2/7x)=0


Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

24x-(+2/7x)-2=0

We get rid of parentheses

24x-2/7x-2=0

We multiply all the terms by the denominator


24x*7x-2*7x-2=0

Wy multiply elements

168x^2-14x-2=0

a = 168; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·168·(-2)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{385}}{2*168}=\frac{14-2\sqrt{385}}{336}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{385}}{2*168}=\frac{14+2\sqrt{385}}{336}
$