1.3x-3.6=4/5.x+2

Solution for 1.3x-3.6=4/5.x+2 equation:

1.3x-3.6=4/5.x+2

We move all terms to the left:

1.3x-3.6-(4/5.x+2)=0


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

x∈R


We get rid of parentheses

1.3x-4/5.x-2-3.6=0

We multiply all the terms by the denominator


(1.3x)*5.x-2*5.x-(3.6)*5.x-4=0

We add all the numbers together, and all the variables

(+1.3x)*5.x-2*5.x-(3.6)*5.x-4=0

We multiply parentheses

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

Wy multiply elements

5x^2-10x-18x-4=0

We add all the numbers together, and all the variables

5x^2-28x-4=0

a = 5; b = -28; c = -4;
Δ = b2-4ac
Δ = -282-4·5·(-4)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-12\sqrt{6}}{2*5}=\frac{28-12\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+12\sqrt{6}}{2*5}=\frac{28+12\sqrt{6}}{10}
$