0=12x^2+34x+10

Solution for 0=12x^2+34x+10 equation:

0=12x^2+34x+10

We move all terms to the left:

0-(12x^2+34x+10)=0

We add all the numbers together, and all the variables

-(12x^2+34x+10)=0

We get rid of parentheses

-12x^2-34x-10=0

a = -12; b = -34; c = -10;
Δ = b2-4ac
Δ = -342-4·(-12)·(-10)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-26}{2*-12}=\frac{8}{-24}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+26}{2*-12}=\frac{60}{-24}
=-2+1/2
$