-43x=-42x^2-6

Solution for -43x=-42x^2-6 equation:

-43x=-42x^2-6

We move all terms to the left:

-43x-(-42x^2-6)=0

We get rid of parentheses

42x^2-43x+6=0

a = 42; b = -43; c = +6;
Δ = b2-4ac
Δ = -432-4·42·6
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-29}{2*42}=\frac{14}{84}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+29}{2*42}=\frac{72}{84}
=6/7
$