7x-43x^2-43x+7=0

Solution for 7x-43x^2-43x+7=0 equation:

7x-43x^2-43x+7=0

We add all the numbers together, and all the variables

-43x^2-36x+7=0

a = -43; b = -36; c = +7;
Δ = b2-4ac
Δ = -362-4·(-43)·7
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-50}{2*-43}=\frac{-14}{-86}
=7/43
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+50}{2*-43}=\frac{86}{-86}
=-1
$