5/4(4x2)=3

Solution for 5/4(4x2)=3 equation:

5/4(4x^2)=3

We move all terms to the left:

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


Domain of the equation: 44x^2!=0

x^2!=0/44

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-3*44x^2+5=0

Wy multiply elements

-132x^2+5=0

a = -132; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-132)·5
Δ = 2640
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:

$\sqrt{\Delta}=\sqrt{2640}=\sqrt{16*165}=\sqrt{16}*\sqrt{165}=4\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{165}}{2*-132}=\frac{0-4\sqrt{165}}{-264}
=-\frac{4\sqrt{165}}{-264}
=-\frac{\sqrt{165}}{-66}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{165}}{2*-132}=\frac{0+4\sqrt{165}}{-264}
=\frac{4\sqrt{165}}{-264}
=\frac{\sqrt{165}}{-66}
$