3/5x-6=18-4x-1

Solution for 3/5x-6=18-4x-1 equation:

3/5x-6=18-4x-1

We move all terms to the left:

3/5x-6-(18-4x-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-(-4x+17)-6=0

We get rid of parentheses

3/5x+4x-17-6=0

We multiply all the terms by the denominator


4x*5x-17*5x-6*5x+3=0

Wy multiply elements

20x^2-85x-30x+3=0

We add all the numbers together, and all the variables

20x^2-115x+3=0

a = 20; b = -115; c = +3;
Δ = b2-4ac
Δ = -1152-4·20·3
Δ = 12985
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:

$\sqrt{\Delta}=\sqrt{12985}=\sqrt{49*265}=\sqrt{49}*\sqrt{265}=7\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115)-7\sqrt{265}}{2*20}=\frac{115-7\sqrt{265}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115)+7\sqrt{265}}{2*20}=\frac{115+7\sqrt{265}}{40}
$