1/3x+5=10x+5

Solution for 1/3x+5=10x+5 equation:

1/3x+5=10x+5

We move all terms to the left:

1/3x+5-(10x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-10x-5+5=0

We multiply all the terms by the denominator


-10x*3x-5*3x+5*3x+1=0

Wy multiply elements

-30x^2-15x+15x+1=0

We add all the numbers together, and all the variables

-30x^2+1=0

a = -30; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-30)·1
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{30}}{2*-30}=\frac{0-2\sqrt{30}}{-60}
=-\frac{2\sqrt{30}}{-60}
=-\frac{\sqrt{30}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{30}}{2*-30}=\frac{0+2\sqrt{30}}{-60}
=\frac{2\sqrt{30}}{-60}
=\frac{\sqrt{30}}{-30}
$