4x-7=31/2x

Solution for 4x-7=31/2x equation:

4x-7=31/2x

We move all terms to the left:

4x-7-(31/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+31/2x)-7=0

We get rid of parentheses

4x-31/2x-7=0

We multiply all the terms by the denominator


4x*2x-7*2x-31=0

Wy multiply elements

8x^2-14x-31=0

a = 8; b = -14; c = -31;
Δ = b2-4ac
Δ = -142-4·8·(-31)
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{33}}{2*8}=\frac{14-6\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{33}}{2*8}=\frac{14+6\sqrt{33}}{16}
$