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x2-7x=2
We move all terms to the left:
x2-7x-(2)=0
We add all the numbers together, and all the variables
x^2-7x-2=0
a = 1; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·1·(-2)
Δ = 57
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{-(-7)-\sqrt{57}}{2*1}=\frac{7-\sqrt{57}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{57}}{2*1}=\frac{7+\sqrt{57}}{2} $
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