0.25(14x-6)=7/2x-15

Solution for 0.25(14x-6)=7/2x-15 equation:

0.25(14x-6)=7/2x-15

We move all terms to the left:

0.25(14x-6)-(7/2x-15)=0


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

x∈R


We multiply parentheses

3.5x-(7/2x-15)-1.5=0

We get rid of parentheses

3.5x-7/2x+15-1.5=0

We multiply all the terms by the denominator


(3.5x)*2x+15*2x-(1.5)*2x-7=0

We add all the numbers together, and all the variables

(+3.5x)*2x+15*2x-(1.5)*2x-7=0

We multiply parentheses

6x^2+15*2x-3x-7=0

Wy multiply elements

6x^2+30x-3x-7=0

We add all the numbers together, and all the variables

6x^2+27x-7=0

a = 6; b = 27; c = -7;
Δ = b2-4ac
Δ = 272-4·6·(-7)
Δ = 897
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{897}}{2*6}=\frac{-27-\sqrt{897}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{897}}{2*6}=\frac{-27+\sqrt{897}}{12}
$