5x^2+6=456

Solution for 5x^2+6=456 equation:

5x^2+6=456

We move all terms to the left:

5x^2+6-(456)=0

We add all the numbers together, and all the variables

5x^2-450=0

a = 5; b = 0; c = -450;
Δ = b2-4ac
Δ = 02-4·5·(-450)
Δ = 9000
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:

$\sqrt{\Delta}=\sqrt{9000}=\sqrt{900*10}=\sqrt{900}*\sqrt{10}=30\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{10}}{2*5}=\frac{0-30\sqrt{10}}{10}
=-\frac{30\sqrt{10}}{10}
=-3\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{10}}{2*5}=\frac{0+30\sqrt{10}}{10}
=\frac{30\sqrt{10}}{10}
=3\sqrt{10}
$