X/4x+7=10+2x

Solution for X/4x+7=10+2x equation:

X/4X+7=10+2X

We move all terms to the left:

X/4X+7-(10+2X)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

X/4X-(2X+10)+7=0

We get rid of parentheses

X/4X-2X-10+7=0

We multiply all the terms by the denominator


X-2X*4X-10*4X+7*4X=0

Wy multiply elements

-8X^2+X-40X+28X=0

We add all the numbers together, and all the variables

-8X^2-11X=0

a = -8; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·(-8)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*-8}=\frac{0}{-16}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*-8}=\frac{22}{-16}
=-1+3/8
$