4=3x^2-10x-9

Solution for 4=3x^2-10x-9 equation:

4=3x^2-10x-9

We move all terms to the left:

4-(3x^2-10x-9)=0

We get rid of parentheses

-3x^2+10x+9+4=0

We add all the numbers together, and all the variables

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

a = -3; b = 10; c = +13;
Δ = b2-4ac
Δ = 102-4·(-3)·13
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-16}{2*-3}=\frac{-26}{-6}
=4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+16}{2*-3}=\frac{6}{-6}
=-1
$