5x-12=-2+5x(x-2)

Solution for 5x-12=-2+5x(x-2) equation:

5x-12=-2+5x(x-2)

We move all terms to the left:

5x-12-(-2+5x(x-2))=0


We calculate terms in parentheses: -(-2+5x(x-2)), so:

-2+5x(x-2)

determiningTheFunctionDomain
5x(x-2)-2

We multiply parentheses

5x^2-10x-2

Back to the equation:

-(5x^2-10x-2)


We get rid of parentheses

-5x^2+5x+10x+2-12=0

We add all the numbers together, and all the variables

-5x^2+15x-10=0

a = -5; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·(-5)·(-10)
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{-(15)-5}{2*-5}=\frac{-20}{-10}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5}{2*-5}=\frac{-10}{-10}
=1
$