12x^2+29x=30+2x^2+9x

Solution for 12x^2+29x=30+2x^2+9x equation:

12x^2+29x=30+2x^2+9x

We move all terms to the left:

12x^2+29x-(30+2x^2+9x)=0

We get rid of parentheses

12x^2-2x^2-9x+29x-30=0

We add all the numbers together, and all the variables

10x^2+20x-30=0

a = 10; b = 20; c = -30;
Δ = b2-4ac
Δ = 202-4·10·(-30)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-40}{2*10}=\frac{-60}{20}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+40}{2*10}=\frac{20}{20}
=1
$