X/2x+15=7x

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

X/2X+15=7X

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-14X^2+31X=0

a = -14; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-14)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-14}=\frac{-62}{-28}
=2+3/14
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-14}=\frac{0}{-28}
=0
$