Y=x^2+5.4x-7

Solution for Y=x^2+5.4x-7 equation:

=Y^2+5.4Y-7

We move all terms to the left:

-(Y^2+5.4Y-7)=0

We get rid of parentheses

-Y^2-5.4Y+7=0

We add all the numbers together, and all the variables

-1Y^2-5.4Y+7=0

a = -1; b = -5.4; c = +7;
Δ = b2-4ac
Δ = -5.42-4·(-1)·7
Δ = 57.16
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{-(-5.4)-\sqrt{57.16}}{2*-1}=\frac{5.4-\sqrt{57.16}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.4)+\sqrt{57.16}}{2*-1}=\frac{5.4+\sqrt{57.16}}{-2}
$