x^2/9=x+4

Solution for x^2/9=x+4 equation:

x^2/9=x+4

We move all terms to the left:

x^2/9-(x+4)=0

We get rid of parentheses

x^2/9-x-4=0

We multiply all the terms by the denominator


x^2-x*9-4*9=0

We add all the numbers together, and all the variables

x^2-x*9-36=0

Wy multiply elements

x^2-9x-36=0

a = 1; b = -9; c = -36;
Δ = b2-4ac
Δ = -92-4·1·(-36)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*1}=\frac{-6}{2}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*1}=\frac{24}{2}
=12
$