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x2-7x-2=30
We move all terms to the left:
x2-7x-2-(30)=0
We add all the numbers together, and all the variables
x^2-7x-32=0
a = 1; b = -7; c = -32;
Δ = b2-4ac
Δ = -72-4·1·(-32)
Δ = 177
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{177}}{2*1}=\frac{7-\sqrt{177}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{177}}{2*1}=\frac{7+\sqrt{177}}{2} $
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