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3=x2-5=78
We move all terms to the left:
3-(x2-5)=0
We add all the numbers together, and all the variables
-(+x^2-5)+3=0
We get rid of parentheses
-x^2+5+3=0
We add all the numbers together, and all the variables
-1x^2+8=0
a = -1; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-1)·8
Δ = 32
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*-1}=\frac{0-4\sqrt{2}}{-2} =-\frac{4\sqrt{2}}{-2} =-\frac{2\sqrt{2}}{-1} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*-1}=\frac{0+4\sqrt{2}}{-2} =\frac{4\sqrt{2}}{-2} =\frac{2\sqrt{2}}{-1} $
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