5x+9=4x^2

Solution for 5x+9=4x^2 equation:

5x+9=4x^2

We move all terms to the left:

5x+9-(4x^2)=0

determiningTheFunctionDomain
-4x^2+5x+9=0

a = -4; b = 5; c = +9;
Δ = b2-4ac
Δ = 52-4·(-4)·9
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*-4}=\frac{-18}{-8}
=2+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*-4}=\frac{8}{-8}
=-1
$