(X)=-x2+6x

Solution for (X)=-x2+6x equation:

(X)=-X2+6X

We move all terms to the left:

(X)-(-X2+6X)=0

We add all the numbers together, and all the variables

-(-1X^2+6X)+X=0

We get rid of parentheses

1X^2-6X+X=0

We add all the numbers together, and all the variables

X^2-5X=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$