x2-9=5(x-3)

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Solution for x2-9=5(x-3) equation:



x2-9=5(x-3)
We move all terms to the left:
x2-9-(5(x-3))=0
We add all the numbers together, and all the variables
x^2-(5(x-3))-9=0
We calculate terms in parentheses: -(5(x-3)), so:
5(x-3)
We multiply parentheses
5x-15
Back to the equation:
-(5x-15)
We get rid of parentheses
x^2-5x+15-9=0
We add all the numbers together, and all the variables
x^2-5x+6=0
a = 1; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·1·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-1}{2*1}=\frac{4}{2} =2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*1}=\frac{6}{2} =3 $

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