x(2x+9)=893

Solution for x(2x+9)=893 equation:

x(2x+9)=893

We move all terms to the left:

x(2x+9)-(893)=0

We multiply parentheses

2x^2+9x-893=0

a = 2; b = 9; c = -893;
Δ = b2-4ac
Δ = 92-4·2·(-893)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-85}{2*2}=\frac{-94}{4}
=-23+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+85}{2*2}=\frac{76}{4}
=19
$