7/8x+4=x

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

7/8x+4=x

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/8x+4=0

We multiply all the terms by the denominator


-1x*8x+4*8x+7=0

Wy multiply elements

-8x^2+32x+7=0

a = -8; b = 32; c = +7;
Δ = b2-4ac
Δ = 322-4·(-8)·7
Δ = 1248
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:

$\sqrt{\Delta}=\sqrt{1248}=\sqrt{16*78}=\sqrt{16}*\sqrt{78}=4\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{78}}{2*-8}=\frac{-32-4\sqrt{78}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{78}}{2*-8}=\frac{-32+4\sqrt{78}}{-16}
$