78-7/8x=4x

Solution for 78-7/8x=4x equation:

78-7/8x=4x

We move all terms to the left:

78-7/8x-(4x)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-4x-7/8x+78=0

We multiply all the terms by the denominator


-4x*8x+78*8x-7=0

Wy multiply elements

-32x^2+624x-7=0

a = -32; b = 624; c = -7;
Δ = b2-4ac
Δ = 6242-4·(-32)·(-7)
Δ = 388480
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:

$\sqrt{\Delta}=\sqrt{388480}=\sqrt{64*6070}=\sqrt{64}*\sqrt{6070}=8\sqrt{6070}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(624)-8\sqrt{6070}}{2*-32}=\frac{-624-8\sqrt{6070}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(624)+8\sqrt{6070}}{2*-32}=\frac{-624+8\sqrt{6070}}{-64}
$