22x2+9=75

Solution for 22x2+9=75 equation:

22x^2+9=75

We move all terms to the left:

22x^2+9-(75)=0

We add all the numbers together, and all the variables

22x^2-66=0

a = 22; b = 0; c = -66;
Δ = b2-4ac
Δ = 02-4·22·(-66)
Δ = 5808
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:

$\sqrt{\Delta}=\sqrt{5808}=\sqrt{1936*3}=\sqrt{1936}*\sqrt{3}=44\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-44\sqrt{3}}{2*22}=\frac{0-44\sqrt{3}}{44}
=-\frac{44\sqrt{3}}{44}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+44\sqrt{3}}{2*22}=\frac{0+44\sqrt{3}}{44}
=\frac{44\sqrt{3}}{44}
=\sqrt{3}
$