5x(x-4)=3

Solution for 5x(x-4)=3 equation:

5x(x-4)=3

We move all terms to the left:

5x(x-4)-(3)=0

We multiply parentheses

5x^2-20x-3=0

a = 5; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·5·(-3)
Δ = 460
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:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{115}}{2*5}=\frac{20-2\sqrt{115}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{115}}{2*5}=\frac{20+2\sqrt{115}}{10}
$