x(5x-4)=864.5

Solution for x(5x-4)=864.5 equation:

x(5x-4)=864.5

We move all terms to the left:

x(5x-4)-(864.5)=0

We add all the numbers together, and all the variables

x(5x-4)-864.5=0

We multiply parentheses

5x^2-4x-864.5=0

a = 5; b = -4; c = -864.5;
Δ = b2-4ac
Δ = -42-4·5·(-864.5)
Δ = 17306
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{-(-4)-\sqrt{17306}}{2*5}=\frac{4-\sqrt{17306}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{17306}}{2*5}=\frac{4+\sqrt{17306}}{10}
$