0,5x*(23-x)=60

Solution for 0,5x*(23-x)=60 equation:

0.5x(23-x)=60

We move all terms to the left:

0.5x(23-x)-(60)=0

We add all the numbers together, and all the variables

0.5x(-1x+23)-60=0

We multiply parentheses

0x^2+0x-60=0

We add all the numbers together, and all the variables

x^2+x-60=0

a = 1; b = 1; c = -60;
Δ = b2-4ac
Δ = 12-4·1·(-60)
Δ = 241
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{-(1)-\sqrt{241}}{2*1}=\frac{-1-\sqrt{241}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{241}}{2*1}=\frac{-1+\sqrt{241}}{2}
$