3x2=12+5x

Solution for 3x2=12+5x equation:

3x^2=12+5x

We move all terms to the left:

3x^2-(12+5x)=0

We add all the numbers together, and all the variables

3x^2-(5x+12)=0

We get rid of parentheses

3x^2-5x-12=0

a = 3; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·3·(-12)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*3}=\frac{-8}{6}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*3}=\frac{18}{6}
=3
$