-3/4x-1.5=2x+15

Solution for -3/4x-1.5=2x+15 equation:

-3/4x-1.5=2x+15

We move all terms to the left:

-3/4x-1.5-(2x+15)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-3/4x-2x-15-1.5=0

We multiply all the terms by the denominator


-2x*4x-15*4x-(1.5)*4x-3=0

We multiply parentheses

-2x*4x-15*4x-6x-3=0

Wy multiply elements

-8x^2-60x-6x-3=0

We add all the numbers together, and all the variables

-8x^2-66x-3=0

a = -8; b = -66; c = -3;
Δ = b2-4ac
Δ = -662-4·(-8)·(-3)
Δ = 4260
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:

$\sqrt{\Delta}=\sqrt{4260}=\sqrt{4*1065}=\sqrt{4}*\sqrt{1065}=2\sqrt{1065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1065}}{2*-8}=\frac{66-2\sqrt{1065}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1065}}{2*-8}=\frac{66+2\sqrt{1065}}{-16}
$