5x-8=3/2x+6

Solution for 5x-8=3/2x+6 equation:

5x-8=3/2x+6

We move all terms to the left:

5x-8-(3/2x+6)=0


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

5x-3/2x-6-8=0

We multiply all the terms by the denominator


5x*2x-6*2x-8*2x-3=0

Wy multiply elements

10x^2-12x-16x-3=0

We add all the numbers together, and all the variables

10x^2-28x-3=0

a = 10; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·10·(-3)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{226}}{2*10}=\frac{28-2\sqrt{226}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{226}}{2*10}=\frac{28+2\sqrt{226}}{20}
$