2x(x-50)=470

Solution for 2x(x-50)=470 equation:

2x(x-50)=470

We move all terms to the left:

2x(x-50)-(470)=0

We multiply parentheses

2x^2-100x-470=0

a = 2; b = -100; c = -470;
Δ = b2-4ac
Δ = -1002-4·2·(-470)
Δ = 13760
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:

$\sqrt{\Delta}=\sqrt{13760}=\sqrt{64*215}=\sqrt{64}*\sqrt{215}=8\sqrt{215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-8\sqrt{215}}{2*2}=\frac{100-8\sqrt{215}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+8\sqrt{215}}{2*2}=\frac{100+8\sqrt{215}}{4}
$