3/4x-3/14x=120

Solution for 3/4x-3/14x=120 equation:

3/4x-3/14x=120

We move all terms to the left:

3/4x-3/14x-(120)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 14x!=0

x!=0/14

x!=0

x∈R


We calculate fractions


42x/56x^2+(-12x)/56x^2-120=0

We multiply all the terms by the denominator


42x+(-12x)-120*56x^2=0

Wy multiply elements

-6720x^2+42x+(-12x)=0

We get rid of parentheses

-6720x^2+42x-12x=0

We add all the numbers together, and all the variables

-6720x^2+30x=0

a = -6720; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-6720)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-6720}=\frac{-60}{-13440}
=1/224
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-6720}=\frac{0}{-13440}
=0
$