-7y-3/10y+6=-6

Solution for -7y-3/10y+6=-6 equation:

-7y-3/10y+6=-6

We move all terms to the left:

-7y-3/10y+6-(-6)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R


We add all the numbers together, and all the variables

-7y-3/10y+12=0

We multiply all the terms by the denominator


-7y*10y+12*10y-3=0

Wy multiply elements

-70y^2+120y-3=0

a = -70; b = 120; c = -3;
Δ = b2-4ac
Δ = 1202-4·(-70)·(-3)
Δ = 13560
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:

$\sqrt{\Delta}=\sqrt{13560}=\sqrt{4*3390}=\sqrt{4}*\sqrt{3390}=2\sqrt{3390}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3390}}{2*-70}=\frac{-120-2\sqrt{3390}}{-140}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3390}}{2*-70}=\frac{-120+2\sqrt{3390}}{-140}
$