42(x^2-1)=13x

Solution for 42(x^2-1)=13x equation:

42(x^2-1)=13x

We move all terms to the left:

42(x^2-1)-(13x)=0

We add all the numbers together, and all the variables

-13x+42(x^2-1)=0

We multiply parentheses

42x^2-13x-42=0

a = 42; b = -13; c = -42;
Δ = b2-4ac
Δ = -132-4·42·(-42)
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-85}{2*42}=\frac{-72}{84}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+85}{2*42}=\frac{98}{84}
=1+1/6
$