340-5x=40-10x+x^2

Solution for 340-5x=40-10x+x^2 equation:

340-5x=40-10x+x^2

We move all terms to the left:

340-5x-(40-10x+x^2)=0

We get rid of parentheses

-x^2+10x-5x-40+340=0

We add all the numbers together, and all the variables

-1x^2+5x+300=0

a = -1; b = 5; c = +300;
Δ = b2-4ac
Δ = 52-4·(-1)·300
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*-1}=\frac{30}{-2}
=-15
$