6a^2-2a+8=-9a+11

Solution for 6a^2-2a+8=-9a+11 equation:

6a^2-2a+8=-9a+11

We move all terms to the left:

6a^2-2a+8-(-9a+11)=0

We get rid of parentheses

6a^2-2a+9a-11+8=0

We add all the numbers together, and all the variables

6a^2+7a-3=0

a = 6; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·6·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*6}=\frac{-18}{12}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*6}=\frac{4}{12}
=1/3
$