x(2x+5)=592

Solution for x(2x+5)=592 equation:

x(2x+5)=592

We move all terms to the left:

x(2x+5)-(592)=0

We multiply parentheses

2x^2+5x-592=0

a = 2; b = 5; c = -592;
Δ = b2-4ac
Δ = 52-4·2·(-592)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-69}{2*2}=\frac{-74}{4}
=-18+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+69}{2*2}=\frac{64}{4}
=16
$