2(x-13)4x+7=15

Solution for 2(x-13)4x+7=15 equation:

2(x-13)4x+7=15

We move all terms to the left:

2(x-13)4x+7-(15)=0

We add all the numbers together, and all the variables

2(x-13)4x-8=0

We multiply parentheses

8x^2-104x-8=0

a = 8; b = -104; c = -8;
Δ = b2-4ac
Δ = -1042-4·8·(-8)
Δ = 11072
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:

$\sqrt{\Delta}=\sqrt{11072}=\sqrt{64*173}=\sqrt{64}*\sqrt{173}=8\sqrt{173}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-8\sqrt{173}}{2*8}=\frac{104-8\sqrt{173}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+8\sqrt{173}}{2*8}=\frac{104+8\sqrt{173}}{16}
$