2(x-7)5x=4

Solution for 2(x-7)5x=4 equation:

2(x-7)5x=4

We move all terms to the left:

2(x-7)5x-(4)=0

We multiply parentheses

10x^2-70x-4=0

a = 10; b = -70; c = -4;
Δ = b2-4ac
Δ = -702-4·10·(-4)
Δ = 5060
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:

$\sqrt{\Delta}=\sqrt{5060}=\sqrt{4*1265}=\sqrt{4}*\sqrt{1265}=2\sqrt{1265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1265}}{2*10}=\frac{70-2\sqrt{1265}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1265}}{2*10}=\frac{70+2\sqrt{1265}}{20}
$