Y(x)=4(x-9/4)+9

Solution for Y(x)=4(x-9/4)+9 equation:

(Y)=4(Y-9/4)+9

We move all terms to the left:

(Y)-(4(Y-9/4)+9)=0

We add all the numbers together, and all the variables

Y-(4(+Y-9/4)+9)=0

We multiply all the terms by the denominator


Y*4)+9)-(4(+Y-9=0

We add all the numbers together, and all the variables

Y+Y*4)+9)-(4(-9=0

Wy multiply elements

4Y^2+Y-9=0

a = 4; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·4·(-9)
Δ = 145
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{145}}{2*4}=\frac{-1-\sqrt{145}}{8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{145}}{2*4}=\frac{-1+\sqrt{145}}{8}
$