3/2x+3=15x+10

Solution for 3/2x+3=15x+10 equation:

3/2x+3=15x+10

We move all terms to the left:

3/2x+3-(15x+10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-15x-10+3=0

We multiply all the terms by the denominator


-15x*2x-10*2x+3*2x+3=0

Wy multiply elements

-30x^2-20x+6x+3=0

We add all the numbers together, and all the variables

-30x^2-14x+3=0

a = -30; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·(-30)·3
Δ = 556
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:

$\sqrt{\Delta}=\sqrt{556}=\sqrt{4*139}=\sqrt{4}*\sqrt{139}=2\sqrt{139}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{139}}{2*-30}=\frac{14-2\sqrt{139}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{139}}{2*-30}=\frac{14+2\sqrt{139}}{-60}
$