90/6y-12y=-210

Solution for 90/6y-12y=-210 equation:

90/6y-12y=-210

We move all terms to the left:

90/6y-12y-(-210)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

-12y+90/6y+210=0

We multiply all the terms by the denominator


-12y*6y+210*6y+90=0

Wy multiply elements

-72y^2+1260y+90=0

a = -72; b = 1260; c = +90;
Δ = b2-4ac
Δ = 12602-4·(-72)·90
Δ = 1613520
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:

$\sqrt{\Delta}=\sqrt{1613520}=\sqrt{1296*1245}=\sqrt{1296}*\sqrt{1245}=36\sqrt{1245}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1260)-36\sqrt{1245}}{2*-72}=\frac{-1260-36\sqrt{1245}}{-144}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1260)+36\sqrt{1245}}{2*-72}=\frac{-1260+36\sqrt{1245}}{-144}
$