4/x=x-6.3

Solution for 4/x=x-6.3 equation:

4/x=x-6.3

We move all terms to the left:

4/x-(x-6.3)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-x+6.3=0

We multiply all the terms by the denominator


-x*x+(6.3)*x+4=0

We multiply parentheses

-x*x+6.3x+4=0

Wy multiply elements

-1x^2+6.3x+4=0

a = -1; b = 6.3; c = +4;
Δ = b2-4ac
Δ = 6.32-4·(-1)·4
Δ = 55.69
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{-(6.3)-\sqrt{55.69}}{2*-1}=\frac{-6.3-\sqrt{55.69}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.3)+\sqrt{55.69}}{2*-1}=\frac{-6.3+\sqrt{55.69}}{-2}
$