y+1/2y-10=425

Solution for y+1/2y-10=425 equation:

y+1/2y-10=425

We move all terms to the left:

y+1/2y-10-(425)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/2y-435=0

We multiply all the terms by the denominator


y*2y-435*2y+1=0

Wy multiply elements

2y^2-870y+1=0

a = 2; b = -870; c = +1;
Δ = b2-4ac
Δ = -8702-4·2·1
Δ = 756892
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:

$\sqrt{\Delta}=\sqrt{756892}=\sqrt{4*189223}=\sqrt{4}*\sqrt{189223}=2\sqrt{189223}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-870)-2\sqrt{189223}}{2*2}=\frac{870-2\sqrt{189223}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-870)+2\sqrt{189223}}{2*2}=\frac{870+2\sqrt{189223}}{4}
$