x/4x+4=2x+10

Solution for x/4x+4=2x+10 equation:

x/4x+4=2x+10

We move all terms to the left:

x/4x+4-(2x+10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

x/4x-2x-10+4=0

We multiply all the terms by the denominator


x-2x*4x-10*4x+4*4x=0

Wy multiply elements

-8x^2+x-40x+16x=0

We add all the numbers together, and all the variables

-8x^2-23x=0

a = -8; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-8)·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*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-8}=\frac{46}{-16}
=-2+7/8
$