-1/4y-3=6y-26

Solution for -1/4y-3=6y-26 equation:

-1/4y-3=6y-26

We move all terms to the left:

-1/4y-3-(6y-26)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

-1/4y-6y+26-3=0

We multiply all the terms by the denominator


-6y*4y+26*4y-3*4y-1=0

Wy multiply elements

-24y^2+104y-12y-1=0

We add all the numbers together, and all the variables

-24y^2+92y-1=0

a = -24; b = 92; c = -1;
Δ = b2-4ac
Δ = 922-4·(-24)·(-1)
Δ = 8368
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:

$\sqrt{\Delta}=\sqrt{8368}=\sqrt{16*523}=\sqrt{16}*\sqrt{523}=4\sqrt{523}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-4\sqrt{523}}{2*-24}=\frac{-92-4\sqrt{523}}{-48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+4\sqrt{523}}{2*-24}=\frac{-92+4\sqrt{523}}{-48}
$