(3/10)x-2x+(4/5)=3/5

Solution for (3/10)x-2x+(4/5)=3/5 equation:

(3/10)x-2x+(4/5)=3/5

We move all terms to the left:

(3/10)x-2x+(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-2x+(+4/5)-(+3/5)=0

We add all the numbers together, and all the variables

-2x+(+3/10)x+(+4/5)-(+3/5)=0

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

15x^2-10x+1=0

a = 15; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·15·1
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{10}}{2*15}=\frac{10-2\sqrt{10}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{10}}{2*15}=\frac{10+2\sqrt{10}}{30}
$