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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(-1+2(x-3)), so:

-1+2(x-3)

determiningTheFunctionDomain
2(x-3)-1

We multiply parentheses

2x-6-1

We add all the numbers together, and all the variables

2x-7

Back to the equation:

-(2x-7)


We add all the numbers together, and all the variables

-1x^2-3x-(2x-7)+5=0

We get rid of parentheses

-1x^2-3x-2x+7+5=0

We add all the numbers together, and all the variables

-1x^2-5x+12=0

a = -1; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-1)·12
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{73}}{2*-1}=\frac{5-\sqrt{73}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*-1}=\frac{5+\sqrt{73}}{-2}
$