7x^2=1-x

Solution for 7x^2=1-x equation:

7x^2=1-x

We move all terms to the left:

7x^2-(1-x)=0

We add all the numbers together, and all the variables

7x^2-(-1x+1)=0

We get rid of parentheses

7x^2+1x-1=0

We add all the numbers together, and all the variables

7x^2+x-1=0

a = 7; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·7·(-1)
Δ = 29
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{29}}{2*7}=\frac{-1-\sqrt{29}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{29}}{2*7}=\frac{-1+\sqrt{29}}{14}
$