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

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

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

We move all terms to the left:

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


Domain of the equation: 5x-2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

25x^2+10x-150x+1=0

We add all the numbers together, and all the variables

25x^2-140x+1=0

a = 25; b = -140; c = +1;
Δ = b2-4ac
Δ = -1402-4·25·1
Δ = 19500
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:

$\sqrt{\Delta}=\sqrt{19500}=\sqrt{100*195}=\sqrt{100}*\sqrt{195}=10\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-10\sqrt{195}}{2*25}=\frac{140-10\sqrt{195}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+10\sqrt{195}}{2*25}=\frac{140+10\sqrt{195}}{50}
$