T(x)=5x^2-7x

Solution for T(x)=5x^2-7x equation:

(T)=5T^2-7T

We move all terms to the left:

(T)-(5T^2-7T)=0

We get rid of parentheses

-5T^2+T+7T=0

We add all the numbers together, and all the variables

-5T^2+8T=0

a = -5; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-5)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-5}=\frac{-16}{-10}
=1+3/5
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-5}=\frac{0}{-10}
=0
$