2x^2-13x=171

Solution for 2x^2-13x=171 equation:

2x^2-13x=171

We move all terms to the left:

2x^2-13x-(171)=0

a = 2; b = -13; c = -171;
Δ = b2-4ac
Δ = -132-4·2·(-171)
Δ = 1537
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{1537}}{2*2}=\frac{13-\sqrt{1537}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{1537}}{2*2}=\frac{13+\sqrt{1537}}{4}
$