13(x-7)5x=131

Solution for 13(x-7)5x=131 equation:

13(x-7)5x=131

We move all terms to the left:

13(x-7)5x-(131)=0

We multiply parentheses

65x^2-455x-131=0

a = 65; b = -455; c = -131;
Δ = b2-4ac
Δ = -4552-4·65·(-131)
Δ = 241085
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{-(-455)-\sqrt{241085}}{2*65}=\frac{455-\sqrt{241085}}{130}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-455)+\sqrt{241085}}{2*65}=\frac{455+\sqrt{241085}}{130}
$