26x(4x-12)=42

Solution for 26x(4x-12)=42 equation:

26x(4x-12)=42

We move all terms to the left:

26x(4x-12)-(42)=0

We multiply parentheses

104x^2-312x-42=0

a = 104; b = -312; c = -42;
Δ = b2-4ac
Δ = -3122-4·104·(-42)
Δ = 114816
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:

$\sqrt{\Delta}=\sqrt{114816}=\sqrt{64*1794}=\sqrt{64}*\sqrt{1794}=8\sqrt{1794}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-312)-8\sqrt{1794}}{2*104}=\frac{312-8\sqrt{1794}}{208}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-312)+8\sqrt{1794}}{2*104}=\frac{312+8\sqrt{1794}}{208}
$