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0=16x^2-114x-28
We move all terms to the left:
0-(16x^2-114x-28)=0
We add all the numbers together, and all the variables
-(16x^2-114x-28)=0
We get rid of parentheses
-16x^2+114x+28=0
a = -16; b = 114; c = +28;
Δ = b2-4ac
Δ = 1142-4·(-16)·28
Δ = 14788
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14788}=\sqrt{4*3697}=\sqrt{4}*\sqrt{3697}=2\sqrt{3697}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-2\sqrt{3697}}{2*-16}=\frac{-114-2\sqrt{3697}}{-32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+2\sqrt{3697}}{2*-16}=\frac{-114+2\sqrt{3697}}{-32} $
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