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0=-16x^2+80-6
We move all terms to the left:
0-(-16x^2+80-6)=0
We add all the numbers together, and all the variables
-(-16x^2+80-6)=0
We get rid of parentheses
16x^2-80+6=0
We add all the numbers together, and all the variables
16x^2-74=0
a = 16; b = 0; c = -74;
Δ = b2-4ac
Δ = 02-4·16·(-74)
Δ = 4736
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4736}=\sqrt{64*74}=\sqrt{64}*\sqrt{74}=8\sqrt{74}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{74}}{2*16}=\frac{0-8\sqrt{74}}{32} =-\frac{8\sqrt{74}}{32} =-\frac{\sqrt{74}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{74}}{2*16}=\frac{0+8\sqrt{74}}{32} =\frac{8\sqrt{74}}{32} =\frac{\sqrt{74}}{4} $
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