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X^2+X^2=12X+44
We move all terms to the left:
X^2+X^2-(12X+44)=0
We add all the numbers together, and all the variables
2X^2-(12X+44)=0
We get rid of parentheses
2X^2-12X-44=0
a = 2; b = -12; c = -44;
Δ = b2-4ac
Δ = -122-4·2·(-44)
Δ = 496
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{31}}{2*2}=\frac{12-4\sqrt{31}}{4} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{31}}{2*2}=\frac{12+4\sqrt{31}}{4} $
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