x^2=3x+45

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Solution for x^2=3x+45 equation:



x^2=3x+45
We move all terms to the left:
x^2-(3x+45)=0
We get rid of parentheses
x^2-3x-45=0
a = 1; b = -3; c = -45;
Δ = b2-4ac
Δ = -32-4·1·(-45)
Δ = 189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{21}}{2*1}=\frac{3-3\sqrt{21}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{21}}{2*1}=\frac{3+3\sqrt{21}}{2} $

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