4a^2-26a+15=0

Solution for 4a^2-26a+15=0 equation:

4a^2-26a+15=0

a = 4; b = -26; c = +15;
Δ = b2-4ac
Δ = -262-4·4·15
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{109}}{2*4}=\frac{26-2\sqrt{109}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{109}}{2*4}=\frac{26+2\sqrt{109}}{8}
$