x*x=4x+9

Solution for x*x=4x+9 equation:

x*x=4x+9

We move all terms to the left:

x*x-(4x+9)=0

Wy multiply elements

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

We get rid of parentheses

x^2-4x-9=0

a = 1; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·1·(-9)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{13}}{2*1}=\frac{4-2\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{13}}{2*1}=\frac{4+2\sqrt{13}}{2}
$