6x^2-10x=10x-5

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

6x^2-10x=10x-5

We move all terms to the left:

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

We get rid of parentheses

6x^2-10x-10x+5=0

We add all the numbers together, and all the variables

6x^2-20x+5=0

a = 6; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·6·5
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{70}}{2*6}=\frac{20-2\sqrt{70}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{70}}{2*6}=\frac{20+2\sqrt{70}}{12}
$