0=3x^2+13x+10

Solution for 0=3x^2+13x+10 equation:

0=3x^2+13x+10

We move all terms to the left:

0-(3x^2+13x+10)=0

We add all the numbers together, and all the variables

-(3x^2+13x+10)=0

We get rid of parentheses

-3x^2-13x-10=0

a = -3; b = -13; c = -10;
Δ = b2-4ac
Δ = -132-4·(-3)·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-7}{2*-3}=\frac{6}{-6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+7}{2*-3}=\frac{20}{-6}
=-3+1/3
$