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X2+4X-9=4

We move all terms to the left:

X2+4X-9-(4)=0

We add all the numbers together, and all the variables

X^2+4X-13=0

a = 1; b = 4; c = -13;

Δ = b^{2}-4ac

Δ = 4^{2}-4·1·(-13)

Δ = 68

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}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{17}}{2*1}=\frac{-4-2\sqrt{17}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{17}}{2*1}=\frac{-4+2\sqrt{17}}{2} $

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