x-3=3/5x+6

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

x-3=3/5x+6

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-30x-15x-3=0

We add all the numbers together, and all the variables

5x^2-45x-3=0

a = 5; b = -45; c = -3;
Δ = b2-4ac
Δ = -452-4·5·(-3)
Δ = 2085
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{-(-45)-\sqrt{2085}}{2*5}=\frac{45-\sqrt{2085}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2085}}{2*5}=\frac{45+\sqrt{2085}}{10}
$