5x2=44x+9

Solution for 5x2=44x+9 equation:

5x^2=44x+9

We move all terms to the left:

5x^2-(44x+9)=0

We get rid of parentheses

5x^2-44x-9=0

a = 5; b = -44; c = -9;
Δ = b2-4ac
Δ = -442-4·5·(-9)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-46}{2*5}=\frac{-2}{10}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+46}{2*5}=\frac{90}{10}
=9
$