26x^2-78x+17=0

Solution for 26x^2-78x+17=0 equation:

26x^2-78x+17=0

a = 26; b = -78; c = +17;
Δ = b2-4ac
Δ = -782-4·26·17
Δ = 4316
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:

$\sqrt{\Delta}=\sqrt{4316}=\sqrt{4*1079}=\sqrt{4}*\sqrt{1079}=2\sqrt{1079}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1079}}{2*26}=\frac{78-2\sqrt{1079}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1079}}{2*26}=\frac{78+2\sqrt{1079}}{52}
$