5x^2=9x+4

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

5x^2=9x+4

We move all terms to the left:

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

We get rid of parentheses

5x^2-9x-4=0

a = 5; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·5·(-4)
Δ = 161
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{161}}{2*5}=\frac{9-\sqrt{161}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{161}}{2*5}=\frac{9+\sqrt{161}}{10}
$