1.2x+1.5=3/8x-6

Solution for 1.2x+1.5=3/8x-6 equation:

1.2x+1.5=3/8x-6

We move all terms to the left:

1.2x+1.5-(3/8x-6)=0


Domain of the equation: 8x-6)!=0

x∈R


We get rid of parentheses

1.2x-3/8x+6+1.5=0

We multiply all the terms by the denominator


(1.2x)*8x+6*8x+(1.5)*8x-3=0

We add all the numbers together, and all the variables

(+1.2x)*8x+6*8x+(1.5)*8x-3=0

We multiply parentheses

8x^2+6*8x+12x-3=0

Wy multiply elements

8x^2+48x+12x-3=0

We add all the numbers together, and all the variables

8x^2+60x-3=0

a = 8; b = 60; c = -3;
Δ = b2-4ac
Δ = 602-4·8·(-3)
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{231}}{2*8}=\frac{-60-4\sqrt{231}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{231}}{2*8}=\frac{-60+4\sqrt{231}}{16}
$