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x=x^2-3x-45
We move all terms to the left:
x-(x^2-3x-45)=0
We get rid of parentheses
-x^2+x+3x+45=0
We add all the numbers together, and all the variables
-1x^2+4x+45=0
a = -1; b = 4; c = +45;
Δ = b2-4ac
Δ = 42-4·(-1)·45
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14}{2*-1}=\frac{-18}{-2} =+9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14}{2*-1}=\frac{10}{-2} =-5 $
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