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-4(5t-3)9t=4t-2
We move all terms to the left:
-4(5t-3)9t-(4t-2)=0
We multiply parentheses
-180t^2+108t-(4t-2)=0
We get rid of parentheses
-180t^2+108t-4t+2=0
We add all the numbers together, and all the variables
-180t^2+104t+2=0
a = -180; b = 104; c = +2;
Δ = b2-4ac
Δ = 1042-4·(-180)·2
Δ = 12256
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}$$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12256}=\sqrt{16*766}=\sqrt{16}*\sqrt{766}=4\sqrt{766}$$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-4\sqrt{766}}{2*-180}=\frac{-104-4\sqrt{766}}{-360} $$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+4\sqrt{766}}{2*-180}=\frac{-104+4\sqrt{766}}{-360} $
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