T=10x(x+5)

Solution for T=10x(x+5) equation:

=10T(T+5)

We move all terms to the left:

-(10T(T+5))=0


We calculate terms in parentheses: -(10T(T+5)), so:

10T(T+5)

We multiply parentheses

10T^2+50T

Back to the equation:

-(10T^2+50T)


We get rid of parentheses

-10T^2-50T=0

a = -10; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·(-10)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*-10}=\frac{0}{-20}
=0
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*-10}=\frac{100}{-20}
=-5
$