2(x-13)4x+7=10

Solution for 2(x-13)4x+7=10 equation:

2(x-13)4x+7=10

We move all terms to the left:

2(x-13)4x+7-(10)=0

We add all the numbers together, and all the variables

2(x-13)4x-3=0

We multiply parentheses

8x^2-104x-3=0

a = 8; b = -104; c = -3;
Δ = b2-4ac
Δ = -1042-4·8·(-3)
Δ = 10912
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:

$\sqrt{\Delta}=\sqrt{10912}=\sqrt{16*682}=\sqrt{16}*\sqrt{682}=4\sqrt{682}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-104)-4\sqrt{682}}{2*8}=\frac{104-4\sqrt{682}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-104)+4\sqrt{682}}{2*8}=\frac{104+4\sqrt{682}}{16}
$