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193=8b^2-7
We move all terms to the left:
193-(8b^2-7)=0
We get rid of parentheses
-8b^2+7+193=0
We add all the numbers together, and all the variables
-8b^2+200=0
a = -8; b = 0; c = +200;
Δ = b2-4ac
Δ = 02-4·(-8)·200
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{6400}=80$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*-8}=\frac{-80}{-16} =+5 $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*-8}=\frac{80}{-16} =-5 $
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