0.75=x+4/x+12

Solution for 0.75=x+4/x+12 equation:

0.75=x+4/x+12

We move all terms to the left:

0.75-(x+4/x+12)=0


Domain of the equation: x+12)!=0

x∈R


We get rid of parentheses

-x-4/x-12+0.75=0

We multiply all the terms by the denominator


-x*x-12*x+(0.75)*x-4=0

We add all the numbers together, and all the variables

-12x-x*x+(0.75)*x-4=0

We multiply parentheses

-12x-x*x+0.75x-4=0

Wy multiply elements

-1x^2-12x+0.75x-4=0

We add all the numbers together, and all the variables

-1x^2-11.25x-4=0

a = -1; b = -11.25; c = -4;
Δ = b2-4ac
Δ = -11.252-4·(-1)·(-4)
Δ = 110.5625
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{-(-11.25)-\sqrt{110.5625}}{2*-1}=\frac{11.25-\sqrt{110.5625}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.25)+\sqrt{110.5625}}{2*-1}=\frac{11.25+\sqrt{110.5625}}{-2}
$