x^2/5=x+9

Solution for x^2/5=x+9 equation:

x^2/5=x+9

We move all terms to the left:

x^2/5-(x+9)=0

We get rid of parentheses

x^2/5-x-9=0

We multiply all the terms by the denominator


x^2-x*5-9*5=0

We add all the numbers together, and all the variables

x^2-x*5-45=0

Wy multiply elements

x^2-5x-45=0

a = 1; b = -5; c = -45;
Δ = b2-4ac
Δ = -52-4·1·(-45)
Δ = 205
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{205}}{2*1}=\frac{5-\sqrt{205}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{205}}{2*1}=\frac{5+\sqrt{205}}{2}
$