-3/2x-1/4x=7

Solution for -3/2x-1/4x=7 equation:

-3/2x-1/4x=7

We move all terms to the left:

-3/2x-1/4x-(7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


(-12x)/8x^2+(-2x)/8x^2-7=0

We multiply all the terms by the denominator


(-12x)+(-2x)-7*8x^2=0

Wy multiply elements

-56x^2+(-12x)+(-2x)=0

We get rid of parentheses

-56x^2-12x-2x=0

We add all the numbers together, and all the variables

-56x^2-14x=0

a = -56; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-56)·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*-56}=\frac{0}{-112}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-56}=\frac{28}{-112}
=-1/4
$