x^2+34x=71000

Solution for x^2+34x=71000 equation:

x^2+34x=71000

We move all terms to the left:

x^2+34x-(71000)=0

a = 1; b = 34; c = -71000;
Δ = b2-4ac
Δ = 342-4·1·(-71000)
Δ = 285156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{285156}=534$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-534}{2*1}=\frac{-568}{2}
=-284
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+534}{2*1}=\frac{500}{2}
=250
$