12/7x-5=24+8x

Solution for 12/7x-5=24+8x equation:

12/7x-5=24+8x

We move all terms to the left:

12/7x-5-(24+8x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

12/7x-(8x+24)-5=0

We get rid of parentheses

12/7x-8x-24-5=0

We multiply all the terms by the denominator


-8x*7x-24*7x-5*7x+12=0

Wy multiply elements

-56x^2-168x-35x+12=0

We add all the numbers together, and all the variables

-56x^2-203x+12=0

a = -56; b = -203; c = +12;
Δ = b2-4ac
Δ = -2032-4·(-56)·12
Δ = 43897
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-203)-\sqrt{43897}}{2*-56}=\frac{203-\sqrt{43897}}{-112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-203)+\sqrt{43897}}{2*-56}=\frac{203+\sqrt{43897}}{-112}
$