X/5x+7/2=3/2x-14

Solution for X/5x+7/2=3/2x-14 equation:

X/5X+7/2=3/2X-14

We move all terms to the left:

X/5X+7/2-(3/2X-14)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R



Domain of the equation: 2X-14)!=0

X∈R


We get rid of parentheses

X/5X-3/2X+14+7/2=0

We calculate fractions


8X^2/40X^2+(-15X)/40X^2+35X/40X^2+14=0

We multiply all the terms by the denominator


8X^2+(-15X)+35X+14*40X^2=0

We add all the numbers together, and all the variables

8X^2+35X+(-15X)+14*40X^2=0

Wy multiply elements

8X^2+560X^2+35X+(-15X)=0

We get rid of parentheses

8X^2+560X^2+35X-15X=0

We add all the numbers together, and all the variables

568X^2+20X=0

a = 568; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·568·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*568}=\frac{-40}{1136}
=-5/142
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*568}=\frac{0}{1136}
=0
$