X=7-5/2x

Solution for X=7-5/2x equation:

X=7-5/2X

We move all terms to the left:

X-(7-5/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(-5/2X+7)=0

We get rid of parentheses

X+5/2X-7=0

We multiply all the terms by the denominator


X*2X-7*2X+5=0

Wy multiply elements

2X^2-14X+5=0

a = 2; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·2·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*2}=\frac{14-2\sqrt{39}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*2}=\frac{14+2\sqrt{39}}{4}
$