16x2-6x2+3=75-3+2x2

Solution for 16x2-6x2+3=75-3+2x2 equation:

16x^2-6x^2+3=75-3+2x^2

We move all terms to the left:

16x^2-6x^2+3-(75-3+2x^2)=0

We add all the numbers together, and all the variables

10x^2-(75-3+2x^2)+3=0

We get rid of parentheses

10x^2-2x^2-75+3+3=0

We add all the numbers together, and all the variables

8x^2-69=0

a = 8; b = 0; c = -69;
Δ = b2-4ac
Δ = 02-4·8·(-69)
Δ = 2208
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:

$\sqrt{\Delta}=\sqrt{2208}=\sqrt{16*138}=\sqrt{16}*\sqrt{138}=4\sqrt{138}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{138}}{2*8}=\frac{0-4\sqrt{138}}{16}
=-\frac{4\sqrt{138}}{16}
=-\frac{\sqrt{138}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{138}}{2*8}=\frac{0+4\sqrt{138}}{16}
=\frac{4\sqrt{138}}{16}
=\frac{\sqrt{138}}{4}
$