8/7x-x+12=4

Solution for 8/7x-x+12=4 equation:

8/7x-x+12=4

We move all terms to the left:

8/7x-x+12-(4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+8/7x+8=0

We multiply all the terms by the denominator


-1x*7x+8*7x+8=0

Wy multiply elements

-7x^2+56x+8=0

a = -7; b = 56; c = +8;
Δ = b2-4ac
Δ = 562-4·(-7)·8
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{210}}{2*-7}=\frac{-56-4\sqrt{210}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{210}}{2*-7}=\frac{-56+4\sqrt{210}}{-14}
$