100x+x2=7500

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Solution for 100x+x2=7500 equation:



100x+x2=7500
We move all terms to the left:
100x+x2-(7500)=0
We add all the numbers together, and all the variables
x^2+100x-7500=0
a = 1; b = 100; c = -7500;
Δ = b2-4ac
Δ = 1002-4·1·(-7500)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-200}{2*1}=\frac{-300}{2} =-150 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+200}{2*1}=\frac{100}{2} =50 $

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