5(2x+3)=4(1-1/2x)-1

Solution for 5(2x+3)=4(1-1/2x)-1 equation:

5(2x+3)=4(1-1/2x)-1

We move all terms to the left:

5(2x+3)-(4(1-1/2x)-1)=0


Domain of the equation: 2x)-1)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5(2x+3)-(4(-1/2x+1)-1)=0

We multiply parentheses

10x-(4(-1/2x+1)-1)+15=0

We multiply all the terms by the denominator


10x*2x+15*2x-1+1)-1)-(4(+1)-1)=0

We add all the numbers together, and all the variables

10x*2x+15*2x-1+1)-1)-(41-1)=0

We add all the numbers together, and all the variables

10x*2x+15*2x=0

Wy multiply elements

20x^2+30x=0

a = 20; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·20·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*20}=\frac{-60}{40}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*20}=\frac{0}{40}
=0
$