5x2-4x=9

Solution for 5x2-4x=9 equation:

5x^2-4x=9

We move all terms to the left:

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

a = 5; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·5·(-9)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*5}=\frac{18}{10}
=1+4/5
$