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5z^2+3z+75z^2=+3z+7
We move all terms to the left:
5z^2+3z+75z^2-(+3z+7)=0
We add all the numbers together, and all the variables
5z^2+75z^2+3z-(3z+7)=0
We add all the numbers together, and all the variables
80z^2+3z-(3z+7)=0
We get rid of parentheses
80z^2+3z-3z-7=0
We add all the numbers together, and all the variables
80z^2-7=0
a = 80; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·80·(-7)
Δ = 2240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{35}}{2*80}=\frac{0-8\sqrt{35}}{160} =-\frac{8\sqrt{35}}{160} =-\frac{\sqrt{35}}{20} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{35}}{2*80}=\frac{0+8\sqrt{35}}{160} =\frac{8\sqrt{35}}{160} =\frac{\sqrt{35}}{20} $
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