24=-(x*x)+10x

Solution for 24=-(x*x)+10x equation:

24=-(x*x)+10x

We move all terms to the left:

24-(-(x*x)+10x)=0

We add all the numbers together, and all the variables

-(-(+x*x)+10x)+24=0


We calculate terms in parentheses: -(-(+x*x)+10x), so:

-(+x*x)+10x

We add all the numbers together, and all the variables

10x-(+x*x)

We get rid of parentheses

10x-x*x

Wy multiply elements

-1x^2+10x

Back to the equation:

-(-1x^2+10x)


We get rid of parentheses

1x^2-10x+24=0

We add all the numbers together, and all the variables

x^2-10x+24=0

a = 1; b = -10; c = +24;
Δ = b2-4ac
Δ = -102-4·1·24
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*1}=\frac{8}{2}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*1}=\frac{12}{2}
=6
$