0.3x-3.6=4/5x+2

Solution for 0.3x-3.6=4/5x+2 equation:

0.3x-3.6=4/5x+2

We move all terms to the left:

0.3x-3.6-(4/5x+2)=0


Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

0.3x-4/5x-2-3.6=0

We multiply all the terms by the denominator


(0.3x)*5x-2*5x-(3.6)*5x-4=0

We add all the numbers together, and all the variables

(+0.3x)*5x-2*5x-(3.6)*5x-4=0

We multiply parentheses

0x^2-2*5x-18x-4=0

Wy multiply elements

0x^2-10x-18x-4=0

We add all the numbers together, and all the variables

x^2-28x-4=0

a = 1; b = -28; c = -4;
Δ = b2-4ac
Δ = -282-4·1·(-4)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-20\sqrt{2}}{2*1}=\frac{28-20\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+20\sqrt{2}}{2*1}=\frac{28+20\sqrt{2}}{2}
$