4a^2+2a=26

Solution for 4a^2+2a=26 equation:

4a^2+2a=26

We move all terms to the left:

4a^2+2a-(26)=0

a = 4; b = 2; c = -26;
Δ = b2-4ac
Δ = 22-4·4·(-26)
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{105}}{2*4}=\frac{-2-2\sqrt{105}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{105}}{2*4}=\frac{-2+2\sqrt{105}}{8}
$