4x=9-5x2

Solution for 4x=9-5x2 equation:

4x=9-5x^2

We move all terms to the left:

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

We get rid of parentheses

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