4x=7/2x+9

Solution for 4x=7/2x+9 equation:

4x=7/2x+9

We move all terms to the left:

4x-(7/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

4x-7/2x-9=0

We multiply all the terms by the denominator


4x*2x-9*2x-7=0

Wy multiply elements

8x^2-18x-7=0

a = 8; b = -18; c = -7;
Δ = b2-4ac
Δ = -182-4·8·(-7)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{137}}{2*8}=\frac{18-2\sqrt{137}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{137}}{2*8}=\frac{18+2\sqrt{137}}{16}
$