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950=-16x^2+1800
We move all terms to the left:
950-(-16x^2+1800)=0
We get rid of parentheses
16x^2-1800+950=0
We add all the numbers together, and all the variables
16x^2-850=0
a = 16; b = 0; c = -850;
Δ = b2-4ac
Δ = 02-4·16·(-850)
Δ = 54400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{54400}=\sqrt{1600*34}=\sqrt{1600}*\sqrt{34}=40\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{34}}{2*16}=\frac{0-40\sqrt{34}}{32} =-\frac{40\sqrt{34}}{32} =-\frac{5\sqrt{34}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{34}}{2*16}=\frac{0+40\sqrt{34}}{32} =\frac{40\sqrt{34}}{32} =\frac{5\sqrt{34}}{4} $
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