x+5x^2/12=1

Solution for x+5x^2/12=1 equation:

x+5x^2/12=1

We move all terms to the left:

x+5x^2/12-(1)=0

We multiply all the terms by the denominator


5x^2+x*12-1*12=0

We add all the numbers together, and all the variables

5x^2+x*12-12=0

Wy multiply elements

5x^2+12x-12=0

a = 5; b = 12; c = -12;
Δ = b2-4ac
Δ = 122-4·5·(-12)
Δ = 384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{6}}{2*5}=\frac{-12-8\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{6}}{2*5}=\frac{-12+8\sqrt{6}}{10}
$