Y=10-x-7x^2

Solution for Y=10-x-7x^2 equation:

=10-Y-7Y^2

We move all terms to the left:

-(10-Y-7Y^2)=0

We get rid of parentheses

7Y^2+Y-10=0

a = 7; b = 1; c = -10;
Δ = b2-4ac
Δ = 12-4·7·(-10)
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{281}}{2*7}=\frac{-1-\sqrt{281}}{14}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{281}}{2*7}=\frac{-1+\sqrt{281}}{14}
$