Y2+17y+144=y2+7y+18=

Solution for Y2+17y+144=y2+7y+18= equation:

2+17Y+144=Y2+7Y+18=

We move all terms to the left:

2+17Y+144-(Y2+7Y+18)=0

We add all the numbers together, and all the variables

-(+Y^2+7Y+18)+17Y+2+144=0

We add all the numbers together, and all the variables

-(+Y^2+7Y+18)+17Y+146=0

We get rid of parentheses

-Y^2-7Y+17Y-18+146=0

We add all the numbers together, and all the variables

-1Y^2+10Y+128=0

a = -1; b = 10; c = +128;
Δ = b2-4ac
Δ = 102-4·(-1)·128
Δ = 612
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{17}}{2*-1}=\frac{-10-6\sqrt{17}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{17}}{2*-1}=\frac{-10+6\sqrt{17}}{-2}
$