0.3x+3/2x=x+7

Solution for 0.3x+3/2x=x+7 equation:

0.3x+3/2x=x+7

We move all terms to the left:

0.3x+3/2x-(x+7)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

0.3x+3/2x-x-7=0

We multiply all the terms by the denominator


(0.3x)*2x-x*2x-7*2x+3=0

We add all the numbers together, and all the variables

(+0.3x)*2x-x*2x-7*2x+3=0

We multiply parentheses

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

Wy multiply elements

0x^2-2x^2-14x+3=0

We add all the numbers together, and all the variables

-1x^2-14x+3=0

a = -1; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·(-1)·3
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{13}}{2*-1}=\frac{14-4\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{13}}{2*-1}=\frac{14+4\sqrt{13}}{-2}
$