x/8x+4=3x+7

Solution for x/8x+4=3x+7 equation:

x/8x+4=3x+7

We move all terms to the left:

x/8x+4-(3x+7)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

x/8x-3x-7+4=0

We multiply all the terms by the denominator


x-3x*8x-7*8x+4*8x=0

Wy multiply elements

-24x^2+x-56x+32x=0

We add all the numbers together, and all the variables

-24x^2-23x=0

a = -24; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-24)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-24}=\frac{46}{-48}
=-23/24
$