4x=1/2x+15

Solution for 4x=1/2x+15 equation:

4x=1/2x+15

We move all terms to the left:

4x-(1/2x+15)=0


Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

4x-1/2x-15=0

We multiply all the terms by the denominator


4x*2x-15*2x-1=0

Wy multiply elements

8x^2-30x-1=0

a = 8; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·8·(-1)
Δ = 932
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:

$\sqrt{\Delta}=\sqrt{932}=\sqrt{4*233}=\sqrt{4}*\sqrt{233}=2\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{233}}{2*8}=\frac{30-2\sqrt{233}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{233}}{2*8}=\frac{30+2\sqrt{233}}{16}
$