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0=x*x-4x-2072
We move all terms to the left:
0-(x*x-4x-2072)=0
We add all the numbers together, and all the variables
-(-4x+x*x-2072)+0=0
We add all the numbers together, and all the variables
-(-4x+x*x-2072)=0
We get rid of parentheses
4x-x*x+2072=0
Wy multiply elements
-1x^2+4x+2072=0
a = -1; b = 4; c = +2072;
Δ = b2-4ac
Δ = 42-4·(-1)·2072
Δ = 8304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8304}=\sqrt{16*519}=\sqrt{16}*\sqrt{519}=4\sqrt{519}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{519}}{2*-1}=\frac{-4-4\sqrt{519}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{519}}{2*-1}=\frac{-4+4\sqrt{519}}{-2} $
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