x(2x+3)=460

Solution for x(2x+3)=460 equation:

x(2x+3)=460

We move all terms to the left:

x(2x+3)-(460)=0

We multiply parentheses

2x^2+3x-460=0

a = 2; b = 3; c = -460;
Δ = b2-4ac
Δ = 32-4·2·(-460)
Δ = 3689
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{3689}}{2*2}=\frac{-3-\sqrt{3689}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{3689}}{2*2}=\frac{-3+\sqrt{3689}}{4}
$