5x/6+2=x^2

Solution for 5x/6+2=x^2 equation:

5x/6+2=x^2

We move all terms to the left:

5x/6+2-(x^2)=0

determiningTheFunctionDomain
-x^2+5x/6+2=0

We add all the numbers together, and all the variables

-1x^2+5x/6+2=0

We multiply all the terms by the denominator


-1x^2*6+5x+2*6=0

We add all the numbers together, and all the variables

-1x^2*6+5x+12=0

Wy multiply elements

-6x^2+5x+12=0

a = -6; b = 5; c = +12;
Δ = b2-4ac
Δ = 52-4·(-6)·12
Δ = 313
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{-(5)-\sqrt{313}}{2*-6}=\frac{-5-\sqrt{313}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{313}}{2*-6}=\frac{-5+\sqrt{313}}{-12}
$