x2+2x-100=x-28

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Solution for x2+2x-100=x-28 equation:



x2+2x-100=x-28
We move all terms to the left:
x2+2x-100-(x-28)=0
We add all the numbers together, and all the variables
x^2+2x-(x-28)-100=0
We get rid of parentheses
x^2+2x-x+28-100=0
We add all the numbers together, and all the variables
x^2+x-72=0
a = 1; b = 1; c = -72;
Δ = b2-4ac
Δ = 12-4·1·(-72)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*1}=\frac{-18}{2} =-9 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*1}=\frac{16}{2} =8 $

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