X/2x+7=15-2x

Solution for X/2x+7=15-2x equation:

X/2X+7=15-2X

We move all terms to the left:

X/2X+7-(15-2X)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X/2X-(-2X+15)+7=0

We get rid of parentheses

X/2X+2X-15+7=0

We multiply all the terms by the denominator


X+2X*2X-15*2X+7*2X=0

Wy multiply elements

4X^2+X-30X+14X=0

We add all the numbers together, and all the variables

4X^2-15X=0

a = 4; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·4·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*4}=\frac{0}{8}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*4}=\frac{30}{8}
=3+3/4
$