4x+6=-3/2x-5

Solution for 4x+6=-3/2x-5 equation:

4x+6=-3/2x-5

We move all terms to the left:

4x+6-(-3/2x-5)=0


Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

4x+3/2x+5+6=0

We multiply all the terms by the denominator


4x*2x+5*2x+6*2x+3=0

Wy multiply elements

8x^2+10x+12x+3=0

We add all the numbers together, and all the variables

8x^2+22x+3=0

a = 8; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·8·3
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{97}}{2*8}=\frac{-22-2\sqrt{97}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{97}}{2*8}=\frac{-22+2\sqrt{97}}{16}
$