4x-3/2x=15

Solution for 4x-3/2x=15 equation:

4x-3/2x=15

We move all terms to the left:

4x-3/2x-(15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-15*2x-3=0

Wy multiply elements

8x^2-30x-3=0

a = 8; b = -30; c = -3;
Δ = b2-4ac
Δ = -302-4·8·(-3)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{249}}{2*8}=\frac{30-2\sqrt{249}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{249}}{2*8}=\frac{30+2\sqrt{249}}{16}
$