1.5x-12=5/2x-15

Solution for 1.5x-12=5/2x-15 equation:

1.5x-12=5/2x-15

We move all terms to the left:

1.5x-12-(5/2x-15)=0


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

x∈R


We get rid of parentheses

1.5x-5/2x+15-12=0

We multiply all the terms by the denominator


(1.5x)*2x+15*2x-12*2x-5=0

We add all the numbers together, and all the variables

(+1.5x)*2x+15*2x-12*2x-5=0

We multiply parentheses

2x^2+15*2x-12*2x-5=0

Wy multiply elements

2x^2+30x-24x-5=0

We add all the numbers together, and all the variables

2x^2+6x-5=0

a = 2; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·2·(-5)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{19}}{2*2}=\frac{-6-2\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{19}}{2*2}=\frac{-6+2\sqrt{19}}{4}
$