X(x-3)=2(10-x)

Solution for X(x-3)=2(10-x) equation:

X(X-3)=2(10-X)

We move all terms to the left:

X(X-3)-(2(10-X))=0

We add all the numbers together, and all the variables

X(X-3)-(2(-1X+10))=0

We multiply parentheses

X^2-3X-(2(-1X+10))=0


We calculate terms in parentheses: -(2(-1X+10)), so:

2(-1X+10)

We multiply parentheses

-2X+20

Back to the equation:

-(-2X+20)


We get rid of parentheses

X^2-3X+2X-20=0

We add all the numbers together, and all the variables

X^2-1X-20=0

a = 1; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·1·(-20)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*1}=\frac{10}{2}
=5
$