1/x=-4x+5

Solution for 1/x=-4x+5 equation:

1/x=-4x+5

We move all terms to the left:

1/x-(-4x+5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

1/x+4x-5=0

We multiply all the terms by the denominator


4x*x-5*x+1=0

We add all the numbers together, and all the variables

-5x+4x*x+1=0

Wy multiply elements

4x^2-5x+1=0

a = 4; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·4·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*4}=\frac{8}{8}
=1
$