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x^2-21x=-57
We move all terms to the left:
x^2-21x-(-57)=0
We add all the numbers together, and all the variables
x^2-21x+57=0
a = 1; b = -21; c = +57;
Δ = b2-4ac
Δ = -212-4·1·57
Δ = 213
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{-(-21)-\sqrt{213}}{2*1}=\frac{21-\sqrt{213}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{213}}{2*1}=\frac{21+\sqrt{213}}{2} $
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