1.4+2.5x=3/15x-0.8

Solution for 1.4+2.5x=3/15x-0.8 equation:

1.4+2.5x=3/15x-0.8

We move all terms to the left:

1.4+2.5x-(3/15x-0.8)=0


Domain of the equation: 15x-0.8)!=0

x∈R


We get rid of parentheses

2.5x-3/15x+0.8+1.4=0

We multiply all the terms by the denominator


(2.5x)*15x+(0.8)*15x+(1.4)*15x-3=0

We add all the numbers together, and all the variables

(+2.5x)*15x+(0.8)*15x+(1.4)*15x-3=0

We multiply parentheses

30x^2+12x+21x-3=0

We add all the numbers together, and all the variables

30x^2+33x-3=0

a = 30; b = 33; c = -3;
Δ = b2-4ac
Δ = 332-4·30·(-3)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{161}}{2*30}=\frac{-33-3\sqrt{161}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{161}}{2*30}=\frac{-33+3\sqrt{161}}{60}
$