232=3x^2+5x

Solution for 232=3x^2+5x equation:

232=3x^2+5x

We move all terms to the left:

232-(3x^2+5x)=0

We get rid of parentheses

-3x^2-5x+232=0

a = -3; b = -5; c = +232;
Δ = b2-4ac
Δ = -52-4·(-3)·232
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-53}{2*-3}=\frac{-48}{-6}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+53}{2*-3}=\frac{58}{-6}
=-9+2/3
$