38x(x-1)=741

Solution for 38x(x-1)=741 equation:

38x(x-1)=741

We move all terms to the left:

38x(x-1)-(741)=0

We multiply parentheses

38x^2-38x-741=0

a = 38; b = -38; c = -741;
Δ = b2-4ac
Δ = -382-4·38·(-741)
Δ = 114076
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:

$\sqrt{\Delta}=\sqrt{114076}=\sqrt{1444*79}=\sqrt{1444}*\sqrt{79}=38\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38\sqrt{79}}{2*38}=\frac{38-38\sqrt{79}}{76}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38\sqrt{79}}{2*38}=\frac{38+38\sqrt{79}}{76}
$