8x=6/x-9.2

Solution for 8x=6/x-9.2 equation:

8x=6/x-9.2

We move all terms to the left:

8x-(6/x-9.2)=0


Domain of the equation: x-9.2)!=0

x∈R


We get rid of parentheses

8x-6/x+9.2=0

We multiply all the terms by the denominator


8x*x+(9.2)*x-6=0

We multiply parentheses

8x*x+9.2x-6=0

Wy multiply elements

8x^2+9.2x-6=0

a = 8; b = 9.2; c = -6;
Δ = b2-4ac
Δ = 9.22-4·8·(-6)
Δ = 276.64
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{-(9.2)-\sqrt{276.64}}{2*8}=\frac{-9.2-\sqrt{276.64}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.2)+\sqrt{276.64}}{2*8}=\frac{-9.2+\sqrt{276.64}}{16}
$