5x^2+32=146

Solution for 5x^2+32=146 equation:

5x^2+32=146

We move all terms to the left:

5x^2+32-(146)=0

We add all the numbers together, and all the variables

5x^2-114=0

a = 5; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·5·(-114)
Δ = 2280
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:

$\sqrt{\Delta}=\sqrt{2280}=\sqrt{4*570}=\sqrt{4}*\sqrt{570}=2\sqrt{570}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{570}}{2*5}=\frac{0-2\sqrt{570}}{10}
=-\frac{2\sqrt{570}}{10}
=-\frac{\sqrt{570}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{570}}{2*5}=\frac{0+2\sqrt{570}}{10}
=\frac{2\sqrt{570}}{10}
=\frac{\sqrt{570}}{5}
$