(7x-41)(7x-31)=0

Solution for (7x-41)(7x-31)=0 equation:

(7x-41)(7x-31)=0

We multiply parentheses ..

(+49x^2-217x-287x+1271)=0

We get rid of parentheses

49x^2-217x-287x+1271=0

We add all the numbers together, and all the variables

49x^2-504x+1271=0

a = 49; b = -504; c = +1271;
Δ = b2-4ac
Δ = -5042-4·49·1271
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-504)-70}{2*49}=\frac{434}{98}
=4+3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-504)+70}{2*49}=\frac{574}{98}
=5+6/7
$