x(2x+3)=560

Solution for x(2x+3)=560 equation:

x(2x+3)=560

We move all terms to the left:

x(2x+3)-(560)=0

We multiply parentheses

2x^2+3x-560=0

a = 2; b = 3; c = -560;
Δ = b2-4ac
Δ = 32-4·2·(-560)
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-67}{2*2}=\frac{-70}{4}
=-17+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+67}{2*2}=\frac{64}{4}
=16
$