(10/3)x+5/4=29/4

Solution for (10/3)x+5/4=29/4 equation:

(10/3)x+5/4=29/4

We move all terms to the left:

(10/3)x+5/4-(29/4)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+10/3)x+5/4-(+29/4)=0

We multiply parentheses

10x^2+5/4-(+29/4)=0

We get rid of parentheses

10x^2+5/4-29/4=0

We multiply all the terms by the denominator


10x^2*4+5-29=0

We add all the numbers together, and all the variables

10x^2*4-24=0

Wy multiply elements

40x^2-24=0

a = 40; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·40·(-24)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*40}=\frac{0-16\sqrt{15}}{80}
=-\frac{16\sqrt{15}}{80}
=-\frac{\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*40}=\frac{0+16\sqrt{15}}{80}
=\frac{16\sqrt{15}}{80}
=\frac{\sqrt{15}}{5}
$