0.8x+.06/x+12=7.72

Solution for 0.8x+.06/x+12=7.72 equation:

0.8x+.06/x+12=7.72

We move all terms to the left:

0.8x+.06/x+12-(7.72)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

0.8x+.06/x+4.28=0

We multiply all the terms by the denominator


(0.8x)*x+(4.28)*x+.06=0

We add all the numbers together, and all the variables

(+0.8x)*x+(4.28)*x+.06=0

We add all the numbers together, and all the variables

(+0.8x)*x+(4.28)*x+0.06=0

We multiply parentheses

0x^2+4.28x+0.06=0

We add all the numbers together, and all the variables

x^2+4.28x+0.06=0

a = 1; b = 4.28; c = +0.06;
Δ = b2-4ac
Δ = 4.282-4·1·0.06
Δ = 18.0784
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{-(4.28)-\sqrt{18.0784}}{2*1}=\frac{-4.28-\sqrt{18.0784}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.28)+\sqrt{18.0784}}{2*1}=\frac{-4.28+\sqrt{18.0784}}{2}
$