Y-25=x(x-15.75)

Solution for Y-25=x(x-15.75) equation:

-25=Y(Y-15.75)

We move all terms to the left:

-25-(Y(Y-15.75))=0


We calculate terms in parentheses: -(Y(Y-15.75)), so:

Y(Y-15.75)

We multiply parentheses

Y^2-15.75Y

Back to the equation:

-(Y^2-15.75Y)


We get rid of parentheses

-Y^2+15.75Y-25=0

We add all the numbers together, and all the variables

-1Y^2+15.75Y-25=0

a = -1; b = 15.75; c = -25;
Δ = b2-4ac
Δ = 15.752-4·(-1)·(-25)
Δ = 148.0625
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{-(15.75)-\sqrt{148.0625}}{2*-1}=\frac{-15.75-\sqrt{148.0625}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15.75)+\sqrt{148.0625}}{2*-1}=\frac{-15.75+\sqrt{148.0625}}{-2}
$