x(2x-9)=-5

Solution for x(2x-9)=-5 equation:

x(2x-9)=-5

We move all terms to the left:

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

We add all the numbers together, and all the variables

x(2x-9)+5=0

We multiply parentheses

2x^2-9x+5=0

a = 2; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·2·5
Δ = 41
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{41}}{2*2}=\frac{9-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{41}}{2*2}=\frac{9+\sqrt{41}}{4}
$