9/4x=x+15

Solution for 9/4x=x+15 equation:

9/4x=x+15

We move all terms to the left:

9/4x-(x+15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

9/4x-x-15=0

We multiply all the terms by the denominator


-x*4x-15*4x+9=0

Wy multiply elements

-4x^2-60x+9=0

a = -4; b = -60; c = +9;
Δ = b2-4ac
Δ = -602-4·(-4)·9
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{26}}{2*-4}=\frac{60-12\sqrt{26}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{26}}{2*-4}=\frac{60+12\sqrt{26}}{-8}
$