5x+6=3/4x+5

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

5x+6=3/4x+5

We move all terms to the left:

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


Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

20x^2-20x+24x-3=0

We add all the numbers together, and all the variables

20x^2+4x-3=0

a = 20; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·20·(-3)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*20}=\frac{-20}{40}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*20}=\frac{12}{40}
=3/10
$