x(2x-10)=40

Solution for x(2x-10)=40 equation:

x(2x-10)=40

We move all terms to the left:

x(2x-10)-(40)=0

We multiply parentheses

2x^2-10x-40=0

a = 2; b = -10; c = -40;
Δ = b2-4ac
Δ = -102-4·2·(-40)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{105}}{2*2}=\frac{10-2\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{105}}{2*2}=\frac{10+2\sqrt{105}}{4}
$