462=2x^2+5x

Solution for 462=2x^2+5x equation:

462=2x^2+5x

We move all terms to the left:

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

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