-2y+3=1/4y+7

Solution for -2y+3=1/4y+7 equation:

-2y+3=1/4y+7

We move all terms to the left:

-2y+3-(1/4y+7)=0


Domain of the equation: 4y+7)!=0

y∈R


We get rid of parentheses

-2y-1/4y-7+3=0

We multiply all the terms by the denominator


-2y*4y-7*4y+3*4y-1=0

Wy multiply elements

-8y^2-28y+12y-1=0

We add all the numbers together, and all the variables

-8y^2-16y-1=0

a = -8; b = -16; c = -1;
Δ = b2-4ac
Δ = -162-4·(-8)·(-1)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{14}}{2*-8}=\frac{16-4\sqrt{14}}{-16}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{14}}{2*-8}=\frac{16+4\sqrt{14}}{-16}
$