5x(x-2)+9=10-3(x+1)

Solution for 5x(x-2)+9=10-3(x+1) equation:

5x(x-2)+9=10-3(x+1)

We move all terms to the left:

5x(x-2)+9-(10-3(x+1))=0

We multiply parentheses

5x^2-10x-(10-3(x+1))+9=0


We calculate terms in parentheses: -(10-3(x+1)), so:

10-3(x+1)

determiningTheFunctionDomain
-3(x+1)+10

We multiply parentheses

-3x-3+10

We add all the numbers together, and all the variables

-3x+7

Back to the equation:

-(-3x+7)


We get rid of parentheses

5x^2-10x+3x-7+9=0

We add all the numbers together, and all the variables

5x^2-7x+2=0

a = 5; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·5·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*5}=\frac{4}{10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*5}=\frac{10}{10}
=1
$