x(2x+9)=656

Solution for x(2x+9)=656 equation:

x(2x+9)=656

We move all terms to the left:

x(2x+9)-(656)=0

We multiply parentheses

2x^2+9x-656=0

a = 2; b = 9; c = -656;
Δ = b2-4ac
Δ = 92-4·2·(-656)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-73}{2*2}=\frac{-82}{4}
=-20+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+73}{2*2}=\frac{64}{4}
=16
$