x^2-14x-10=6x-1

Solution for x^2-14x-10=6x-1 equation:

x^2-14x-10=6x-1

We move all terms to the left:

x^2-14x-10-(6x-1)=0

We get rid of parentheses

x^2-14x-6x+1-10=0

We add all the numbers together, and all the variables

x^2-20x-9=0

a = 1; b = -20; c = -9;
Δ = b2-4ac
Δ = -202-4·1·(-9)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{109}}{2*1}=\frac{20-2\sqrt{109}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{109}}{2*1}=\frac{20+2\sqrt{109}}{2}
$