X=4y-3/2y+5

Solution for X=4y-3/2y+5 equation:

X=4X-3/2X+5

We move all terms to the left:

X-(4X-3/2X+5)=0


Domain of the equation: 2X+5)!=0

X∈R


We get rid of parentheses

X-4X+3/2X-5=0

We multiply all the terms by the denominator


X*2X-4X*2X-5*2X+3=0

Wy multiply elements

2X^2-8X^2-10X+3=0

We add all the numbers together, and all the variables

-6X^2-10X+3=0

a = -6; b = -10; c = +3;
Δ = b2-4ac
Δ = -102-4·(-6)·3
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{43}}{2*-6}=\frac{10-2\sqrt{43}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{43}}{2*-6}=\frac{10+2\sqrt{43}}{-12}
$