6x^2-10x=5

Solution for 6x^2-10x=5 equation:

6x^2-10x=5

We move all terms to the left:

6x^2-10x-(5)=0

a = 6; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·6·(-5)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{55}}{2*6}=\frac{10-2\sqrt{55}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{55}}{2*6}=\frac{10+2\sqrt{55}}{12}
$