-310=x(x-40)

Solution for -310=x(x-40) equation:

-310=x(x-40)

We move all terms to the left:

-310-(x(x-40))=0


We calculate terms in parentheses: -(x(x-40)), so:

x(x-40)

We multiply parentheses

x^2-40x

Back to the equation:

-(x^2-40x)


We get rid of parentheses

-x^2+40x-310=0

We add all the numbers together, and all the variables

-1x^2+40x-310=0

a = -1; b = 40; c = -310;
Δ = b2-4ac
Δ = 402-4·(-1)·(-310)
Δ = 360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-6\sqrt{10}}{2*-1}=\frac{-40-6\sqrt{10}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+6\sqrt{10}}{2*-1}=\frac{-40+6\sqrt{10}}{-2}
$