X2-5x=12(12-x)

Solution for X2-5x=12(12-x) equation:

X2-5X=12(12-X)

We move all terms to the left:

X2-5X-(12(12-X))=0

We add all the numbers together, and all the variables

X2-5X-(12(-1X+12))=0

We add all the numbers together, and all the variables

X^2-5X-(12(-1X+12))=0


We calculate terms in parentheses: -(12(-1X+12)), so:

12(-1X+12)

We multiply parentheses

-12X+144

Back to the equation:

-(-12X+144)


We get rid of parentheses

X^2-5X+12X-144=0

We add all the numbers together, and all the variables

X^2+7X-144=0

a = 1; b = 7; c = -144;
Δ = b2-4ac
Δ = 72-4·1·(-144)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-25}{2*1}=\frac{-32}{2}
=-16
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+25}{2*1}=\frac{18}{2}
=9
$