3/5x-27.5=1.2x-0.5

Solution for 3/5x-27.5=1.2x-0.5 equation:

3/5x-27.5=1.2x-0.5

We move all terms to the left:

3/5x-27.5-(1.2x-0.5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-1.2x+0.5-27.5=0

We multiply all the terms by the denominator


-(1.2x)*5x+(0.5)*5x-(27.5)*5x+3=0

We add all the numbers together, and all the variables

-(+1.2x)*5x+(0.5)*5x-(27.5)*5x+3=0

We multiply parentheses

-5x^2+2.5x-137.5x+3=0

We add all the numbers together, and all the variables

-5x^2-135x+3=0

a = -5; b = -135; c = +3;
Δ = b2-4ac
Δ = -1352-4·(-5)·3
Δ = 18285
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-\sqrt{18285}}{2*-5}=\frac{135-\sqrt{18285}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18285}}{2*-5}=\frac{135+\sqrt{18285}}{-10}
$