X/2X+4(2x+7)=2x+4

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

X/2X+4(2X+7)=2X+4

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply parentheses

X/2X+8X-(2X+4)+28=0

We get rid of parentheses

X/2X+8X-2X-4+28=0

We multiply all the terms by the denominator


X+8X*2X-2X*2X-4*2X+28*2X=0

Wy multiply elements

16X^2-4X^2+X-8X+56X=0

We add all the numbers together, and all the variables

12X^2+49X=0

a = 12; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·12·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*12}=\frac{-98}{24}
=-4+1/12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*12}=\frac{0}{24}
=0
$