x(2x+5)=462

Solution for x(2x+5)=462 equation:

x(2x+5)=462

We move all terms to the left:

x(2x+5)-(462)=0

We multiply parentheses

2x^2+5x-462=0

a = 2; b = 5; c = -462;
Δ = b2-4ac
Δ = 52-4·2·(-462)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-61}{2*2}=\frac{-66}{4}
=-16+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+61}{2*2}=\frac{56}{4}
=14
$