-2(4x-1)13x+5=-26

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Solution for -2(4x-1)13x+5=-26 equation:



-2(4x-1)13x+5=-26
We move all terms to the left:
-2(4x-1)13x+5-(-26)=0
We add all the numbers together, and all the variables
-2(4x-1)13x+31=0
We multiply parentheses
-104x^2+26x+31=0
a = -104; b = 26; c = +31;
Δ = b2-4ac
Δ = 262-4·(-104)·31
Δ = 13572
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:
$\sqrt{\Delta}=\sqrt{13572}=\sqrt{36*377}=\sqrt{36}*\sqrt{377}=6\sqrt{377}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-6\sqrt{377}}{2*-104}=\frac{-26-6\sqrt{377}}{-208} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+6\sqrt{377}}{2*-104}=\frac{-26+6\sqrt{377}}{-208} $

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