X-6=7/2x+4

Solution for X-6=7/2x+4 equation:

X-6=7/2X+4

We move all terms to the left:

X-6-(7/2X+4)=0


Domain of the equation: 2X+4)!=0

X∈R


We get rid of parentheses

X-7/2X-4-6=0

We multiply all the terms by the denominator


X*2X-4*2X-6*2X-7=0

Wy multiply elements

2X^2-8X-12X-7=0

We add all the numbers together, and all the variables

2X^2-20X-7=0

a = 2; b = -20; c = -7;
Δ = b2-4ac
Δ = -202-4·2·(-7)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{114}}{2*2}=\frac{20-2\sqrt{114}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{114}}{2*2}=\frac{20+2\sqrt{114}}{4}
$