4/5*x-65/100*x=21

Solution for 4/5*x-65/100*x=21 equation:

4/5x-65/100x=21

We move all terms to the left:

4/5x-65/100x-(21)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We calculate fractions


400x/500x^2+(-325x)/500x^2-21=0

We multiply all the terms by the denominator


400x+(-325x)-21*500x^2=0

Wy multiply elements

-10500x^2+400x+(-325x)=0

We get rid of parentheses

-10500x^2+400x-325x=0

We add all the numbers together, and all the variables

-10500x^2+75x=0

a = -10500; b = 75; c = 0;
Δ = b2-4ac
Δ = 752-4·(-10500)·0
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-75}{2*-10500}=\frac{-150}{-21000}
=1/140
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+75}{2*-10500}=\frac{0}{-21000}
=0
$