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0=900-240x-12x^2
We move all terms to the left:
0-(900-240x-12x^2)=0
We add all the numbers together, and all the variables
-(900-240x-12x^2)=0
We get rid of parentheses
12x^2+240x-900=0
a = 12; b = 240; c = -900;
Δ = b2-4ac
Δ = 2402-4·12·(-900)
Δ = 100800
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{100800}=\sqrt{14400*7}=\sqrt{14400}*\sqrt{7}=120\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-120\sqrt{7}}{2*12}=\frac{-240-120\sqrt{7}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+120\sqrt{7}}{2*12}=\frac{-240+120\sqrt{7}}{24} $
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