5x2+4=9x+2x2

Solution for 5x2+4=9x+2x2 equation:

5x^2+4=9x+2x^2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-9x+4=0

a = 3; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·3·4
Δ = 33
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{-(-9)-\sqrt{33}}{2*3}=\frac{9-\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{33}}{2*3}=\frac{9+\sqrt{33}}{6}
$