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

Solution for 6x^2+6=-7x+11 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+7x-5=0

a = 6; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·6·(-5)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*6}=\frac{-20}{12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*6}=\frac{6}{12}
=1/2
$