(x-700)x=1057

Solution for (x-700)x=1057 equation:

(x-700)x=1057

We move all terms to the left:

(x-700)x-(1057)=0

We multiply parentheses

x^2-700x-1057=0

a = 1; b = -700; c = -1057;
Δ = b2-4ac
Δ = -7002-4·1·(-1057)
Δ = 494228
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:

$\sqrt{\Delta}=\sqrt{494228}=\sqrt{4*123557}=\sqrt{4}*\sqrt{123557}=2\sqrt{123557}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-700)-2\sqrt{123557}}{2*1}=\frac{700-2\sqrt{123557}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-700)+2\sqrt{123557}}{2*1}=\frac{700+2\sqrt{123557}}{2}
$