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(x^2)-x=2x+3
We move all terms to the left:
(x^2)-x-(2x+3)=0
We add all the numbers together, and all the variables
x^2-1x-(2x+3)=0
We get rid of parentheses
x^2-1x-2x-3=0
We add all the numbers together, and all the variables
x^2-3x-3=0
a = 1; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·1·(-3)
Δ = 21
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{-(-3)-\sqrt{21}}{2*1}=\frac{3-\sqrt{21}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*1}=\frac{3+\sqrt{21}}{2} $
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