7x^2-46x-17=4

Solution for 7x^2-46x-17=4 equation:

7x^2-46x-17=4

We move all terms to the left:

7x^2-46x-17-(4)=0

We add all the numbers together, and all the variables

7x^2-46x-21=0

a = 7; b = -46; c = -21;
Δ = b2-4ac
Δ = -462-4·7·(-21)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-52}{2*7}=\frac{-6}{14}
=-3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+52}{2*7}=\frac{98}{14}
=7
$