8-7q^2=6-q

Solution for 8-7q^2=6-q equation:

8-7q^2=6-q

We move all terms to the left:

8-7q^2-(6-q)=0

We add all the numbers together, and all the variables

-7q^2-(-1q+6)+8=0

We get rid of parentheses

-7q^2+1q-6+8=0

We add all the numbers together, and all the variables

-7q^2+q+2=0

a = -7; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-7)·2
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{57}}{2*-7}=\frac{-1-\sqrt{57}}{-14}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*-7}=\frac{-1+\sqrt{57}}{-14}
$