5x^2-(3/4)x=17/4

Solution for 5x^2-(3/4)x=17/4 equation:

5x^2-(3/4)x=17/4

We move all terms to the left:

5x^2-(3/4)x-(17/4)=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

5x^2-(+3/4)x-(+17/4)=0

We multiply parentheses

5x^2-3x^2-(+17/4)=0

We get rid of parentheses

5x^2-3x^2-17/4=0

We multiply all the terms by the denominator


5x^2*4-3x^2*4-17=0

Wy multiply elements

20x^2-12x^2-17=0

We add all the numbers together, and all the variables

8x^2-17=0

a = 8; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·8·(-17)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{34}}{2*8}=\frac{0-4\sqrt{34}}{16}
=-\frac{4\sqrt{34}}{16}
=-\frac{\sqrt{34}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{34}}{2*8}=\frac{0+4\sqrt{34}}{16}
=\frac{4\sqrt{34}}{16}
=\frac{\sqrt{34}}{4}
$