3/4(x)-21/40(x)=144

Solution for 3/4(x)-21/40(x)=144 equation:

3/4(x)-21/40(x)=144

We move all terms to the left:

3/4(x)-21/40(x)-(144)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 40x!=0

x!=0/40

x!=0

x∈R


We calculate fractions


120x/160x^2+(-84x)/160x^2-144=0

We multiply all the terms by the denominator


120x+(-84x)-144*160x^2=0

Wy multiply elements

-23040x^2+120x+(-84x)=0

We get rid of parentheses

-23040x^2+120x-84x=0

We add all the numbers together, and all the variables

-23040x^2+36x=0

a = -23040; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-23040)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-23040}=\frac{-72}{-46080}
=1/640
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-23040}=\frac{0}{-46080}
=0
$