X+3/2y-4=6

Solution for X+3/2y-4=6 equation:

X+3/2X-4=6

We move all terms to the left:

X+3/2X-4-(6)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+3/2X-10=0

We multiply all the terms by the denominator


X*2X-10*2X+3=0

Wy multiply elements

2X^2-20X+3=0

a = 2; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·2·3
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{94}}{2*2}=\frac{20-2\sqrt{94}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{94}}{2*2}=\frac{20+2\sqrt{94}}{4}
$