-3x-22=-25/x

Solution for -3x-22=-25/x equation:

-3x-22=-25/x

We move all terms to the left:

-3x-22-(-25/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-3x+25/x-22=0

We multiply all the terms by the denominator


-3x*x-22*x+25=0

We add all the numbers together, and all the variables

-22x-3x*x+25=0

Wy multiply elements

-3x^2-22x+25=0

a = -3; b = -22; c = +25;
Δ = b2-4ac
Δ = -222-4·(-3)·25
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-28}{2*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+28}{2*-3}=\frac{50}{-6}
=-8+1/3
$