15x(13x-10)=x-14

Solution for 15x(13x-10)=x-14 equation:

15x(13x-10)=x-14

We move all terms to the left:

15x(13x-10)-(x-14)=0

We multiply parentheses

195x^2-150x-(x-14)=0

We get rid of parentheses

195x^2-150x-x+14=0

We add all the numbers together, and all the variables

195x^2-151x+14=0

a = 195; b = -151; c = +14;
Δ = b2-4ac
Δ = -1512-4·195·14
Δ = 11881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11881}=109$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-151)-109}{2*195}=\frac{42}{390}
=7/65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-151)+109}{2*195}=\frac{260}{390}
=2/3
$