X(4-x)+5x=x2+3x

Solution for X(4-x)+5x=x2+3x equation:

X(4-X)+5X=X2+3X

We move all terms to the left:

X(4-X)+5X-(X2+3X)=0

We add all the numbers together, and all the variables

-(+X^2+3X)+X(-1X+4)+5X=0

We add all the numbers together, and all the variables

-(+X^2+3X)+5X+X(-1X+4)=0

We multiply parentheses

-(+X^2+3X)-1X^2+5X+4X=0

We get rid of parentheses

-X^2-1X^2-3X+5X+4X=0

We add all the numbers together, and all the variables

-2X^2+6X=0

a = -2; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-2)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-2}=\frac{-12}{-4}
=+3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-2}=\frac{0}{-4}
=0
$