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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+5/2x+7=0

We calculate fractions


6x/8x^2+20x/8x^2+7=0

We multiply all the terms by the denominator


6x+20x+7*8x^2=0

We add all the numbers together, and all the variables

26x+7*8x^2=0

Wy multiply elements

56x^2+26x=0

a = 56; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·56·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*56}=\frac{-52}{112}
=-13/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*56}=\frac{0}{112}
=0
$