2x^2+9x=71

Solution for 2x^2+9x=71 equation:

2x^2+9x=71

We move all terms to the left:

2x^2+9x-(71)=0

a = 2; b = 9; c = -71;
Δ = b2-4ac
Δ = 92-4·2·(-71)
Δ = 649
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{-(9)-\sqrt{649}}{2*2}=\frac{-9-\sqrt{649}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{649}}{2*2}=\frac{-9+\sqrt{649}}{4}
$