(5x)^2=x+3

Solution for (5x)^2=x+3 equation:

(5x)^2=x+3

We move all terms to the left:

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

We get rid of parentheses

5x^2-x-3=0

We add all the numbers together, and all the variables

5x^2-1x-3=0

a = 5; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·5·(-3)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{61}}{2*5}=\frac{1-\sqrt{61}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{61}}{2*5}=\frac{1+\sqrt{61}}{10}
$