5x+10/4=5(x2)

Solution for 5x+10/4=5(x2) equation:

5x+10/4=5(x2)

We move all terms to the left:

5x+10/4-(5(x2))=0

determiningTheFunctionDomain
5x-5x2+10/4=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-20x^2+20x+10=0

a = -20; b = 20; c = +10;
Δ = b2-4ac
Δ = 202-4·(-20)·10
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{3}}{2*-20}=\frac{-20-20\sqrt{3}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{3}}{2*-20}=\frac{-20+20\sqrt{3}}{-40}
$