5x^2-25=420

Solution for 5x^2-25=420 equation:

5x^2-25=420

We move all terms to the left:

5x^2-25-(420)=0

We add all the numbers together, and all the variables

5x^2-445=0

a = 5; b = 0; c = -445;
Δ = b2-4ac
Δ = 02-4·5·(-445)
Δ = 8900
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:

$\sqrt{\Delta}=\sqrt{8900}=\sqrt{100*89}=\sqrt{100}*\sqrt{89}=10\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{89}}{2*5}=\frac{0-10\sqrt{89}}{10}
=-\frac{10\sqrt{89}}{10}
=-\sqrt{89}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{89}}{2*5}=\frac{0+10\sqrt{89}}{10}
=\frac{10\sqrt{89}}{10}
=\sqrt{89}
$