x(x-47)=1704

Solution for x(x-47)=1704 equation:

x(x-47)=1704

We move all terms to the left:

x(x-47)-(1704)=0

We multiply parentheses

x^2-47x-1704=0

a = 1; b = -47; c = -1704;
Δ = b2-4ac
Δ = -472-4·1·(-1704)
Δ = 9025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9025}=95$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-95}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+95}{2*1}=\frac{142}{2}
=71
$