3/4x-6=5/2x+7

Solution for 3/4x-6=5/2x+7 equation:

3/4x-6=5/2x+7

We move all terms to the left:

3/4x-6-(5/2x+7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

3/4x-5/2x-7-6=0

We calculate fractions


6x/8x^2+(-20x)/8x^2-7-6=0

We add all the numbers together, and all the variables

6x/8x^2+(-20x)/8x^2-13=0

We multiply all the terms by the denominator


6x+(-20x)-13*8x^2=0

Wy multiply elements

-104x^2+6x+(-20x)=0

We get rid of parentheses

-104x^2+6x-20x=0

We add all the numbers together, and all the variables

-104x^2-14x=0

a = -104; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-104)·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*-104}=\frac{0}{-208}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-104}=\frac{28}{-208}
=-7/52
$