13x(2x-1)=140

Solution for 13x(2x-1)=140 equation:

13x(2x-1)=140

We move all terms to the left:

13x(2x-1)-(140)=0

We multiply parentheses

26x^2-13x-140=0

a = 26; b = -13; c = -140;
Δ = b2-4ac
Δ = -132-4·26·(-140)
Δ = 14729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{14729}}{2*26}=\frac{13-\sqrt{14729}}{52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{14729}}{2*26}=\frac{13+\sqrt{14729}}{52}
$