26x^2-78x+48=0

Solution for 26x^2-78x+48=0 equation:

26x^2-78x+48=0

a = 26; b = -78; c = +48;
Δ = b2-4ac
Δ = -782-4·26·48
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{273}}{2*26}=\frac{78-2\sqrt{273}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{273}}{2*26}=\frac{78+2\sqrt{273}}{52}
$