0=-10x^2+130x-400

Solution for 0=-10x^2+130x-400 equation:

0=-10x^2+130x-400

We move all terms to the left:

0-(-10x^2+130x-400)=0

We add all the numbers together, and all the variables

-(-10x^2+130x-400)=0

We get rid of parentheses

10x^2-130x+400=0

a = 10; b = -130; c = +400;
Δ = b2-4ac
Δ = -1302-4·10·400
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-30}{2*10}=\frac{100}{20}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+30}{2*10}=\frac{160}{20}
=8
$