(9t+47)(9t+47)=121

Solution for (9t+47)(9t+47)=121 equation:

(9t+47)(9t+47)=121

We move all terms to the left:

(9t+47)(9t+47)-(121)=0

We multiply parentheses ..

(+81t^2+423t+423t+2209)-121=0

We get rid of parentheses

81t^2+423t+423t+2209-121=0

We add all the numbers together, and all the variables

81t^2+846t+2088=0

a = 81; b = 846; c = +2088;
Δ = b2-4ac
Δ = 8462-4·81·2088
Δ = 39204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39204}=198$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(846)-198}{2*81}=\frac{-1044}{162}
=-6+4/9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(846)+198}{2*81}=\frac{-648}{162}
=-4
$