-5x(X-3)+6=4-(X-2)

Solution for -5x(X-3)+6=4-(X-2) equation:

-5x(x-3)+6=4-(x-2)

We move all terms to the left:

-5x(x-3)+6-(4-(x-2))=0

We multiply parentheses

-5x^2+15x-(4-(x-2))+6=0


We calculate terms in parentheses: -(4-(x-2)), so:

4-(x-2)

determiningTheFunctionDomain
-(x-2)+4

We get rid of parentheses

-x+2+4

We add all the numbers together, and all the variables

-1x+6

Back to the equation:

-(-1x+6)


We get rid of parentheses

-5x^2+15x+1x-6+6=0

We add all the numbers together, and all the variables

-5x^2+16x=0

a = -5; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-5)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-5}=\frac{-32}{-10}
=3+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-5}=\frac{0}{-10}
=0
$