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36+2x=8+x2
We move all terms to the left:
36+2x-(8+x2)=0
We add all the numbers together, and all the variables
-(+x^2+8)+2x+36=0
We get rid of parentheses
-x^2+2x-8+36=0
We add all the numbers together, and all the variables
-1x^2+2x+28=0
a = -1; b = 2; c = +28;
Δ = b2-4ac
Δ = 22-4·(-1)·28
Δ = 116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{29}}{2*-1}=\frac{-2-2\sqrt{29}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{29}}{2*-1}=\frac{-2+2\sqrt{29}}{-2} $
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