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x*x+12x-9600=0
We add all the numbers together, and all the variables
12x+x*x-9600=0
Wy multiply elements
x^2+12x-9600=0
a = 1; b = 12; c = -9600;
Δ = b2-4ac
Δ = 122-4·1·(-9600)
Δ = 38544
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{38544}=\sqrt{16*2409}=\sqrt{16}*\sqrt{2409}=4\sqrt{2409}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{2409}}{2*1}=\frac{-12-4\sqrt{2409}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{2409}}{2*1}=\frac{-12+4\sqrt{2409}}{2} $
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