T(x)=-x2+24x-106

Solution for T(x)=-x2+24x-106 equation:

(T)=-T2+24T-106

We move all terms to the left:

(T)-(-T2+24T-106)=0

We add all the numbers together, and all the variables

-(-1T^2+24T-106)+T=0

We get rid of parentheses

1T^2-24T+T+106=0

We add all the numbers together, and all the variables

T^2-23T+106=0

a = 1; b = -23; c = +106;
Δ = b2-4ac
Δ = -232-4·1·106
Δ = 105
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{-(-23)-\sqrt{105}}{2*1}=\frac{23-\sqrt{105}}{2}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{105}}{2*1}=\frac{23+\sqrt{105}}{2}
$