4x(x-3)=41

Solution for 4x(x-3)=41 equation:

4x(x-3)=41

We move all terms to the left:

4x(x-3)-(41)=0

We multiply parentheses

4x^2-12x-41=0

a = 4; b = -12; c = -41;
Δ = b2-4ac
Δ = -122-4·4·(-41)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20\sqrt{2}}{2*4}=\frac{12-20\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20\sqrt{2}}{2*4}=\frac{12+20\sqrt{2}}{8}
$