(3/10)x-4x+4/5=3/5

Solution for (3/10)x-4x+4/5=3/5 equation:

(3/10)x-4x+4/5=3/5

We move all terms to the left:

(3/10)x-4x+4/5-(3/5)=0


Domain of the equation: 10)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/10)x-4x+4/5-(+3/5)=0

We add all the numbers together, and all the variables

-4x+(+3/10)x+4/5-(+3/5)=0

We multiply parentheses

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

We get rid of parentheses

3x^2-4x+4/5-3/5=0

We multiply all the terms by the denominator


3x^2*5-4x*5+4-3=0

We add all the numbers together, and all the variables

3x^2*5-4x*5+1=0

Wy multiply elements

15x^2-20x+1=0

a = 15; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·15·1
Δ = 340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{85}}{2*15}=\frac{20-2\sqrt{85}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{85}}{2*15}=\frac{20+2\sqrt{85}}{30}
$