7x^2-51x-46=-6

Solution for 7x^2-51x-46=-6 equation:

7x^2-51x-46=-6

We move all terms to the left:

7x^2-51x-46-(-6)=0

We add all the numbers together, and all the variables

7x^2-51x-40=0

a = 7; b = -51; c = -40;
Δ = b2-4ac
Δ = -512-4·7·(-40)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-61}{2*7}=\frac{-10}{14}
=-5/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+61}{2*7}=\frac{112}{14}
=8
$