-1/5x+30=2x+3

Solution for -1/5x+30=2x+3 equation:

-1/5x+30=2x+3

We move all terms to the left:

-1/5x+30-(2x+3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

-1/5x-2x-3+30=0

We multiply all the terms by the denominator


-2x*5x-3*5x+30*5x-1=0

Wy multiply elements

-10x^2-15x+150x-1=0

We add all the numbers together, and all the variables

-10x^2+135x-1=0

a = -10; b = 135; c = -1;
Δ = b2-4ac
Δ = 1352-4·(-10)·(-1)
Δ = 18185
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{-(135)-\sqrt{18185}}{2*-10}=\frac{-135-\sqrt{18185}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+\sqrt{18185}}{2*-10}=\frac{-135+\sqrt{18185}}{-20}
$