x.2(2x+1)=26

Solution for x.2(2x+1)=26 equation:

x.2(2x+1)=26

We move all terms to the left:

x.2(2x+1)-(26)=0

We multiply parentheses

2x^2+x-26=0

a = 2; b = 1; c = -26;
Δ = b2-4ac
Δ = 12-4·2·(-26)
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{209}}{2*2}=\frac{-1-\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{209}}{2*2}=\frac{-1+\sqrt{209}}{4}
$