X(7-4y)=5y-1

Solution for X(7-4y)=5y-1 equation:

X(7-4X)=5X-1

We move all terms to the left:

X(7-4X)-(5X-1)=0

We add all the numbers together, and all the variables

X(-4X+7)-(5X-1)=0

We multiply parentheses

-4X^2+7X-(5X-1)=0

We get rid of parentheses

-4X^2+7X-5X+1=0

We add all the numbers together, and all the variables

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

a = -4; b = 2; c = +1;
Δ = b2-4ac
Δ = 22-4·(-4)·1
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{5}}{2*-4}=\frac{-2-2\sqrt{5}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{5}}{2*-4}=\frac{-2+2\sqrt{5}}{-8}
$