x(2x+5)=817

Solution for x(2x+5)=817 equation:

x(2x+5)=817

We move all terms to the left:

x(2x+5)-(817)=0

We multiply parentheses

2x^2+5x-817=0

a = 2; b = 5; c = -817;
Δ = b2-4ac
Δ = 52-4·2·(-817)
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-81}{2*2}=\frac{-86}{4}
=-21+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+81}{2*2}=\frac{76}{4}
=19
$