180=(9y+7)(2y+98)

Solution for 180=(9y+7)(2y+98) equation:

180=(9y+7)(2y+98)

We move all terms to the left:

180-((9y+7)(2y+98))=0

We multiply parentheses ..

-((+18y^2+882y+14y+686))+180=0


We calculate terms in parentheses: -((+18y^2+882y+14y+686)), so:

(+18y^2+882y+14y+686)

We get rid of parentheses

18y^2+882y+14y+686

We add all the numbers together, and all the variables

18y^2+896y+686

Back to the equation:

-(18y^2+896y+686)


We get rid of parentheses

-18y^2-896y-686+180=0

We add all the numbers together, and all the variables

-18y^2-896y-506=0

a = -18; b = -896; c = -506;
Δ = b2-4ac
Δ = -8962-4·(-18)·(-506)
Δ = 766384
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:

$\sqrt{\Delta}=\sqrt{766384}=\sqrt{16*47899}=\sqrt{16}*\sqrt{47899}=4\sqrt{47899}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-896)-4\sqrt{47899}}{2*-18}=\frac{896-4\sqrt{47899}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-896)+4\sqrt{47899}}{2*-18}=\frac{896+4\sqrt{47899}}{-36}
$