7.7x^2=1-x

Solution for 7.7x^2=1-x equation:

7.7x^2=1-x

We move all terms to the left:

7.7x^2-(1-x)=0

We add all the numbers together, and all the variables

7.7x^2-(-1x+1)=0

We get rid of parentheses

7.7x^2+1x-1=0

We add all the numbers together, and all the variables

7.7x^2+x-1=0

a = 7.7; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·7.7·(-1)
Δ = 31.8
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{31.8}}{2*7.7}=\frac{-1-\sqrt{31.8}}{15.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{31.8}}{2*7.7}=\frac{-1+\sqrt{31.8}}{15.4}
$