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2t(t+10.5)+90=180
We move all terms to the left:
2t(t+10.5)+90-(180)=0
We add all the numbers together, and all the variables
2t(t+10.5)-90=0
We multiply parentheses
2t^2+21t-90=0
a = 2; b = 21; c = -90;
Δ = b2-4ac
Δ = 212-4·2·(-90)
Δ = 1161
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{129}}{2*2}=\frac{-21-3\sqrt{129}}{4} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{129}}{2*2}=\frac{-21+3\sqrt{129}}{4} $
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