Y=4+7x+-5x2

Solution for Y=4+7x+-5x2 equation:

=4+7Y+-5Y^2

We move all terms to the left:

-(4+7Y+-5Y^2)=0

We use the square of the difference formula

-(4+7Y-5Y^2)=0

We get rid of parentheses

5Y^2-7Y-4=0

a = 5; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·5·(-4)
Δ = 129
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{-(-7)-\sqrt{129}}{2*5}=\frac{7-\sqrt{129}}{10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*5}=\frac{7+\sqrt{129}}{10}
$