6x^2-47x+15=13

Solution for 6x^2-47x+15=13 equation:

6x^2-47x+15=13

We move all terms to the left:

6x^2-47x+15-(13)=0

We add all the numbers together, and all the variables

6x^2-47x+2=0

a = 6; b = -47; c = +2;
Δ = b2-4ac
Δ = -472-4·6·2
Δ = 2161
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{-(-47)-\sqrt{2161}}{2*6}=\frac{47-\sqrt{2161}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2161}}{2*6}=\frac{47+\sqrt{2161}}{12}
$