5/2x+7;2=3/4x+14

Solution for 5/2x+7;2=3/4x+14 equation:

5/2x+72=3/4x+14

We move all terms to the left:

5/2x+72-(3/4x+14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+14)!=0

x∈R


We get rid of parentheses

5/2x-3/4x-14+72=0

We calculate fractions


20x/8x^2+(-6x)/8x^2-14+72=0

We add all the numbers together, and all the variables

20x/8x^2+(-6x)/8x^2+58=0

We multiply all the terms by the denominator


20x+(-6x)+58*8x^2=0

Wy multiply elements

464x^2+20x+(-6x)=0

We get rid of parentheses

464x^2+20x-6x=0

We add all the numbers together, and all the variables

464x^2+14x=0

a = 464; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·464·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*464}=\frac{-28}{928}
=-7/232
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*464}=\frac{0}{928}
=0
$