8/4x+4=7x/16x-6

Solution for 8/4x+4=7x/16x-6 equation:

8/4x+4=7x/16x-6

We move all terms to the left:

8/4x+4-(7x/16x-6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 16x-6)!=0

x∈R


We get rid of parentheses

8/4x-7x/16x+6+4=0

We calculate fractions


(-28x^2)/64x^2+128x/64x^2+6+4=0

We add all the numbers together, and all the variables

(-28x^2)/64x^2+128x/64x^2+10=0

We multiply all the terms by the denominator


(-28x^2)+128x+10*64x^2=0

Wy multiply elements

(-28x^2)+640x^2+128x=0

We get rid of parentheses

-28x^2+640x^2+128x=0

We add all the numbers together, and all the variables

612x^2+128x=0

a = 612; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·612·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*612}=\frac{-256}{1224}
=-32/153
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*612}=\frac{0}{1224}
=0
$