4x=3/2x+29

Solution for 4x=3/2x+29 equation:

4x=3/2x+29

We move all terms to the left:

4x-(3/2x+29)=0


Domain of the equation: 2x+29)!=0

x∈R


We get rid of parentheses

4x-3/2x-29=0

We multiply all the terms by the denominator


4x*2x-29*2x-3=0

Wy multiply elements

8x^2-58x-3=0

a = 8; b = -58; c = -3;
Δ = b2-4ac
Δ = -582-4·8·(-3)
Δ = 3460
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:

$\sqrt{\Delta}=\sqrt{3460}=\sqrt{4*865}=\sqrt{4}*\sqrt{865}=2\sqrt{865}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{865}}{2*8}=\frac{58-2\sqrt{865}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{865}}{2*8}=\frac{58+2\sqrt{865}}{16}
$