3/8x+1.5x=69

Solution for 3/8x+1.5x=69 equation:

3/8x+1.5x=69

We move all terms to the left:

3/8x+1.5x-(69)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

1.5x+3/8x-69=0

We multiply all the terms by the denominator


(1.5x)*8x-69*8x+3=0

We add all the numbers together, and all the variables

(+1.5x)*8x-69*8x+3=0

We multiply parentheses

8x^2-69*8x+3=0

Wy multiply elements

8x^2-552x+3=0

a = 8; b = -552; c = +3;
Δ = b2-4ac
Δ = -5522-4·8·3
Δ = 304608
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:

$\sqrt{\Delta}=\sqrt{304608}=\sqrt{16*19038}=\sqrt{16}*\sqrt{19038}=4\sqrt{19038}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-552)-4\sqrt{19038}}{2*8}=\frac{552-4\sqrt{19038}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-552)+4\sqrt{19038}}{2*8}=\frac{552+4\sqrt{19038}}{16}
$