4/7y-10=y

Solution for 4/7y-10=y equation:

4/7y-10=y

We move all terms to the left:

4/7y-10-(y)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+4/7y-10=0

We multiply all the terms by the denominator


-1y*7y-10*7y+4=0

Wy multiply elements

-7y^2-70y+4=0

a = -7; b = -70; c = +4;
Δ = b2-4ac
Δ = -702-4·(-7)·4
Δ = 5012
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:

$\sqrt{\Delta}=\sqrt{5012}=\sqrt{4*1253}=\sqrt{4}*\sqrt{1253}=2\sqrt{1253}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1253}}{2*-7}=\frac{70-2\sqrt{1253}}{-14}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1253}}{2*-7}=\frac{70+2\sqrt{1253}}{-14}
$