-1x-1/3x+5=-25

Solution for -1x-1/3x+5=-25 equation:

-1x-1/3x+5=-25

We move all terms to the left:

-1x-1/3x+5-(-25)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+90x-1=0

a = -3; b = 90; c = -1;
Δ = b2-4ac
Δ = 902-4·(-3)·(-1)
Δ = 8088
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:

$\sqrt{\Delta}=\sqrt{8088}=\sqrt{4*2022}=\sqrt{4}*\sqrt{2022}=2\sqrt{2022}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2022}}{2*-3}=\frac{-90-2\sqrt{2022}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2022}}{2*-3}=\frac{-90+2\sqrt{2022}}{-6}
$