3/5x+4=12x-3+1

Solution for 3/5x+4=12x-3+1 equation:

3/5x+4=12x-3+1

We move all terms to the left:

3/5x+4-(12x-3+1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3/5x-(12x-2)+4=0

We get rid of parentheses

3/5x-12x+2+4=0

We multiply all the terms by the denominator


-12x*5x+2*5x+4*5x+3=0

Wy multiply elements

-60x^2+10x+20x+3=0

We add all the numbers together, and all the variables

-60x^2+30x+3=0

a = -60; b = 30; c = +3;
Δ = b2-4ac
Δ = 302-4·(-60)·3
Δ = 1620
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:

$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18\sqrt{5}}{2*-60}=\frac{-30-18\sqrt{5}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18\sqrt{5}}{2*-60}=\frac{-30+18\sqrt{5}}{-120}
$