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x(x+7)=133
We move all terms to the left:
x(x+7)-(133)=0
We multiply parentheses
x^2+7x-133=0
a = 1; b = 7; c = -133;
Δ = b2-4ac
Δ = 72-4·1·(-133)
Δ = 581
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{581}}{2*1}=\frac{-7-\sqrt{581}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{581}}{2*1}=\frac{-7+\sqrt{581}}{2} $
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