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x^2+12x-49=84
We move all terms to the left:
x^2+12x-49-(84)=0
We add all the numbers together, and all the variables
x^2+12x-133=0
a = 1; b = 12; c = -133;
Δ = b2-4ac
Δ = 122-4·1·(-133)
Δ = 676
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{676}=26$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-26}{2*1}=\frac{-38}{2} =-19 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+26}{2*1}=\frac{14}{2} =7 $
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