X=7/2x-8

Solution for X=7/2x-8 equation:

X=7/2X-8

We move all terms to the left:

X-(7/2X-8)=0


Domain of the equation: 2X-8)!=0

X∈R


We get rid of parentheses

X-7/2X+8=0

We multiply all the terms by the denominator


X*2X+8*2X-7=0

Wy multiply elements

2X^2+16X-7=0

a = 2; b = 16; c = -7;
Δ = b2-4ac
Δ = 162-4·2·(-7)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{78}}{2*2}=\frac{-16-2\sqrt{78}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{78}}{2*2}=\frac{-16+2\sqrt{78}}{4}
$