7x(2x-1)=35

Solution for 7x(2x-1)=35 equation:

7x(2x-1)=35

We move all terms to the left:

7x(2x-1)-(35)=0

We multiply parentheses

14x^2-7x-35=0

a = 14; b = -7; c = -35;
Δ = b2-4ac
Δ = -72-4·14·(-35)
Δ = 2009
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:

$\sqrt{\Delta}=\sqrt{2009}=\sqrt{49*41}=\sqrt{49}*\sqrt{41}=7\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7\sqrt{41}}{2*14}=\frac{7-7\sqrt{41}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7\sqrt{41}}{2*14}=\frac{7+7\sqrt{41}}{28}
$