9x+900=4x^2

Solution for 9x+900=4x^2 equation:

9x+900=4x^2

We move all terms to the left:

9x+900-(4x^2)=0

determiningTheFunctionDomain
-4x^2+9x+900=0

a = -4; b = 9; c = +900;
Δ = b2-4ac
Δ = 92-4·(-4)·900
Δ = 14481
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:

$\sqrt{\Delta}=\sqrt{14481}=\sqrt{9*1609}=\sqrt{9}*\sqrt{1609}=3\sqrt{1609}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{1609}}{2*-4}=\frac{-9-3\sqrt{1609}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{1609}}{2*-4}=\frac{-9+3\sqrt{1609}}{-8}
$