X=3y+1/4y-7

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

X=3X+1/4X-7

We move all terms to the left:

X-(3X+1/4X-7)=0


Domain of the equation: 4X-7)!=0

X∈R


We get rid of parentheses

X-3X-1/4X+7=0

We multiply all the terms by the denominator


X*4X-3X*4X+7*4X-1=0

Wy multiply elements

4X^2-12X^2+28X-1=0

We add all the numbers together, and all the variables

-8X^2+28X-1=0

a = -8; b = 28; c = -1;
Δ = b2-4ac
Δ = 282-4·(-8)·(-1)
Δ = 752
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{47}}{2*-8}=\frac{-28-4\sqrt{47}}{-16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{47}}{2*-8}=\frac{-28+4\sqrt{47}}{-16}
$