52-5x^2=7

Solution for 52-5x^2=7 equation:

52-5x^2=7

We move all terms to the left:

52-5x^2-(7)=0

We add all the numbers together, and all the variables

-5x^2+45=0

a = -5; b = 0; c = +45;
Δ = b2-4ac
Δ = 02-4·(-5)·45
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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