105=2x^2-26x

Solution for 105=2x^2-26x equation:

105=2x^2-26x

We move all terms to the left:

105-(2x^2-26x)=0

We get rid of parentheses

-2x^2+26x+105=0

a = -2; b = 26; c = +105;
Δ = b2-4ac
Δ = 262-4·(-2)·105
Δ = 1516
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:

$\sqrt{\Delta}=\sqrt{1516}=\sqrt{4*379}=\sqrt{4}*\sqrt{379}=2\sqrt{379}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{379}}{2*-2}=\frac{-26-2\sqrt{379}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{379}}{2*-2}=\frac{-26+2\sqrt{379}}{-4}
$