T(x)=-1/3x+10

Solution for T(x)=-1/3x+10 equation:

(T)=-1/3T+10

We move all terms to the left:

(T)-(-1/3T+10)=0


Domain of the equation: 3T+10)!=0

T∈R


We get rid of parentheses

T+1/3T-10=0

We multiply all the terms by the denominator


T*3T-10*3T+1=0

Wy multiply elements

3T^2-30T+1=0

a = 3; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·3·1
Δ = 888
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:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{222}}{2*3}=\frac{30-2\sqrt{222}}{6}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{222}}{2*3}=\frac{30+2\sqrt{222}}{6}
$