x-1=3/5x+6

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

x-1=3/5x+6

We move all terms to the left:

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


Domain of the equation: 5x+6)!=0

x∈R


We get rid of parentheses

x-3/5x-6-1=0

We multiply all the terms by the denominator


x*5x-6*5x-1*5x-3=0

Wy multiply elements

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

We add all the numbers together, and all the variables

5x^2-35x-3=0

a = 5; b = -35; c = -3;
Δ = b2-4ac
Δ = -352-4·5·(-3)
Δ = 1285
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{-(-35)-\sqrt{1285}}{2*5}=\frac{35-\sqrt{1285}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1285}}{2*5}=\frac{35+\sqrt{1285}}{10}
$