X/3=7x/2x-15

Solution for X/3=7x/2x-15 equation:

X/3=7X/2X-15

We move all terms to the left:

X/3-(7X/2X-15)=0


Domain of the equation: 2X-15)!=0

X∈R


We get rid of parentheses

X/3-7X/2X+15=0

We calculate fractions


2X^2/6X+(-21X)/6X+15=0

We multiply all the terms by the denominator


2X^2+(-21X)+15*6X=0

Wy multiply elements

2X^2+(-21X)+90X=0

We get rid of parentheses

2X^2-21X+90X=0

We add all the numbers together, and all the variables

2X^2+69X=0

a = 2; b = 69; c = 0;
Δ = b2-4ac
Δ = 692-4·2·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-69}{2*2}=\frac{-138}{4}
=-34+1/2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+69}{2*2}=\frac{0}{4}
=0
$