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4x+12=x^2-8x+20
We move all terms to the left:
4x+12-(x^2-8x+20)=0
We get rid of parentheses
-x^2+4x+8x-20+12=0
We add all the numbers together, and all the variables
-1x^2+12x-8=0
a = -1; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·(-1)·(-8)
Δ = 112
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{7}}{2*-1}=\frac{-12-4\sqrt{7}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{7}}{2*-1}=\frac{-12+4\sqrt{7}}{-2} $
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