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10=9t^2/5
We move all terms to the left:
10-(9t^2/5)=0
We get rid of parentheses
-9t^2/5+10=0
We multiply all the terms by the denominator
-9t^2+10*5=0
We add all the numbers together, and all the variables
-9t^2+50=0
a = -9; b = 0; c = +50;
Δ = b2-4ac
Δ = 02-4·(-9)·50
Δ = 1800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*-9}=\frac{0-30\sqrt{2}}{-18} =-\frac{30\sqrt{2}}{-18} =-\frac{5\sqrt{2}}{-3} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*-9}=\frac{0+30\sqrt{2}}{-18} =\frac{30\sqrt{2}}{-18} =\frac{5\sqrt{2}}{-3} $
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