7x^2+3=45

Solution for 7x^2+3=45 equation:

7x^2+3=45

We move all terms to the left:

7x^2+3-(45)=0

We add all the numbers together, and all the variables

7x^2-42=0

a = 7; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·7·(-42)
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{6}}{2*7}=\frac{0-14\sqrt{6}}{14}
=-\frac{14\sqrt{6}}{14}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{6}}{2*7}=\frac{0+14\sqrt{6}}{14}
=\frac{14\sqrt{6}}{14}
=\sqrt{6}
$