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-t=9(t-10)t=
We move all terms to the left:
-t-(9(t-10)t)=0
We add all the numbers together, and all the variables
-1t-(9(t-10)t)=0
We calculate terms in parentheses: -(9(t-10)t), so:We get rid of parentheses
9(t-10)t
We multiply parentheses
9t^2-90t
Back to the equation:
-(9t^2-90t)
-9t^2-1t+90t=0
We add all the numbers together, and all the variables
-9t^2+89t=0
a = -9; b = 89; c = 0;
Δ = b2-4ac
Δ = 892-4·(-9)·0
Δ = 7921
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{7921}=89$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(89)-89}{2*-9}=\frac{-178}{-18} =9+8/9 $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(89)+89}{2*-9}=\frac{0}{-18} =0 $
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