3/5x-6=1x+4

Solution for 3/5x-6=1x+4 equation:

3/5x-6=1x+4

We move all terms to the left:

3/5x-6-(1x+4)=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-(x+4)-6=0

We get rid of parentheses

3/5x-x-4-6=0

We multiply all the terms by the denominator


-x*5x-4*5x-6*5x+3=0

Wy multiply elements

-5x^2-20x-30x+3=0

We add all the numbers together, and all the variables

-5x^2-50x+3=0

a = -5; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·(-5)·3
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-16\sqrt{10}}{2*-5}=\frac{50-16\sqrt{10}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+16\sqrt{10}}{2*-5}=\frac{50+16\sqrt{10}}{-10}
$