5x2-20=3(5x)

Solution for 5x2-20=3(5x) equation:

5x^2-20=3(5x)

We move all terms to the left:

5x^2-20-(3(5x))=0

determiningTheFunctionDomain
5x^2-35x-20=0

a = 5; b = -35; c = -20;
Δ = b2-4ac
Δ = -352-4·5·(-20)
Δ = 1625
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:

$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{65}}{2*5}=\frac{35-5\sqrt{65}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{65}}{2*5}=\frac{35+5\sqrt{65}}{10}
$