2x(x-10)=55

Solution for 2x(x-10)=55 equation:

2x(x-10)=55

We move all terms to the left:

2x(x-10)-(55)=0

We multiply parentheses

2x^2-20x-55=0

a = 2; b = -20; c = -55;
Δ = b2-4ac
Δ = -202-4·2·(-55)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{210}}{2*2}=\frac{20-2\sqrt{210}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{210}}{2*2}=\frac{20+2\sqrt{210}}{4}
$