7x2-47=x2-6x-11

Solution for 7x2-47=x2-6x-11 equation:

7x^2-47=x2-6x-11

We move all terms to the left:

7x^2-47-(x2-6x-11)=0

We add all the numbers together, and all the variables

7x^2-(+x^2-6x-11)-47=0

We get rid of parentheses

7x^2-x^2+6x+11-47=0

We add all the numbers together, and all the variables

6x^2+6x-36=0

a = 6; b = 6; c = -36;
Δ = b2-4ac
Δ = 62-4·6·(-36)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-30}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*6}=\frac{24}{12}
=2
$