(5t+7)17t=55

Solution for (5t+7)17t=55 equation:

(5t+7)17t=55

We move all terms to the left:

(5t+7)17t-(55)=0

We multiply parentheses

85t^2+119t-55=0

a = 85; b = 119; c = -55;
Δ = b2-4ac
Δ = 1192-4·85·(-55)
Δ = 32861
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(119)-\sqrt{32861}}{2*85}=\frac{-119-\sqrt{32861}}{170}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(119)+\sqrt{32861}}{2*85}=\frac{-119+\sqrt{32861}}{170}
$