2x(x+41)=163

Solution for 2x(x+41)=163 equation:

2x(x+41)=163

We move all terms to the left:

2x(x+41)-(163)=0

We multiply parentheses

2x^2+82x-163=0

a = 2; b = 82; c = -163;
Δ = b2-4ac
Δ = 822-4·2·(-163)
Δ = 8028
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:

$\sqrt{\Delta}=\sqrt{8028}=\sqrt{36*223}=\sqrt{36}*\sqrt{223}=6\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-6\sqrt{223}}{2*2}=\frac{-82-6\sqrt{223}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+6\sqrt{223}}{2*2}=\frac{-82+6\sqrt{223}}{4}
$