3x^2-13x+4=10

Solution for 3x^2-13x+4=10 equation:

3x^2-13x+4=10

We move all terms to the left:

3x^2-13x+4-(10)=0

We add all the numbers together, and all the variables

3x^2-13x-6=0

a = 3; b = -13; c = -6;
Δ = b2-4ac
Δ = -132-4·3·(-6)
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{241}}{2*3}=\frac{13-\sqrt{241}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{241}}{2*3}=\frac{13+\sqrt{241}}{6}
$