231x+3619=3x^2+134x+1363

Solution for 231x+3619=3x^2+134x+1363 equation:

231x+3619=3x^2+134x+1363

We move all terms to the left:

231x+3619-(3x^2+134x+1363)=0

We get rid of parentheses

-3x^2+231x-134x-1363+3619=0

We add all the numbers together, and all the variables

-3x^2+97x+2256=0

a = -3; b = 97; c = +2256;
Δ = b2-4ac
Δ = 972-4·(-3)·2256
Δ = 36481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36481}=191$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(97)-191}{2*-3}=\frac{-288}{-6}
=+48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+191}{2*-3}=\frac{94}{-6}
=-15+2/3
$