3-(3/4)x=5/8

Solution for 3-(3/4)x=5/8 equation:

3-(3/4)x=5/8

We move all terms to the left:

3-(3/4)x-(5/8)=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+3/4)x+3-(+5/8)=0

We multiply parentheses

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

We get rid of parentheses

-3x^2+3-5/8=0

We multiply all the terms by the denominator


-3x^2*8-5+3*8=0

We add all the numbers together, and all the variables

-3x^2*8+19=0

Wy multiply elements

-24x^2+19=0

a = -24; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-24)·19
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{114}}{2*-24}=\frac{0-4\sqrt{114}}{-48}
=-\frac{4\sqrt{114}}{-48}
=-\frac{\sqrt{114}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{114}}{2*-24}=\frac{0+4\sqrt{114}}{-48}
=\frac{4\sqrt{114}}{-48}
=\frac{\sqrt{114}}{-12}
$