4/6x+15=3x

Solution for 4/6x+15=3x equation:

4/6x+15=3x

We move all terms to the left:

4/6x+15-(3x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+4/6x+15=0

We multiply all the terms by the denominator


-3x*6x+15*6x+4=0

Wy multiply elements

-18x^2+90x+4=0

a = -18; b = 90; c = +4;
Δ = b2-4ac
Δ = 902-4·(-18)·4
Δ = 8388
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:

$\sqrt{\Delta}=\sqrt{8388}=\sqrt{36*233}=\sqrt{36}*\sqrt{233}=6\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{233}}{2*-18}=\frac{-90-6\sqrt{233}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{233}}{2*-18}=\frac{-90+6\sqrt{233}}{-36}
$