6x^2-10x+6=15

Solution for 6x^2-10x+6=15 equation:

6x^2-10x+6=15

We move all terms to the left:

6x^2-10x+6-(15)=0

We add all the numbers together, and all the variables

6x^2-10x-9=0

a = 6; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·6·(-9)
Δ = 316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{79}}{2*6}=\frac{10-2\sqrt{79}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{79}}{2*6}=\frac{10+2\sqrt{79}}{12}
$