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4x+13=x2-4
We move all terms to the left:
4x+13-(x2-4)=0
We add all the numbers together, and all the variables
-(+x^2-4)+4x+13=0
We get rid of parentheses
-x^2+4x+4+13=0
We add all the numbers together, and all the variables
-1x^2+4x+17=0
a = -1; b = 4; c = +17;
Δ = b2-4ac
Δ = 42-4·(-1)·17
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{21}}{2*-1}=\frac{-4-2\sqrt{21}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{21}}{2*-1}=\frac{-4+2\sqrt{21}}{-2} $
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