75x^2-766+80=0

Solution for 75x^2-766+80=0 equation:

75x^2-766+80=0

We add all the numbers together, and all the variables

75x^2-686=0

a = 75; b = 0; c = -686;
Δ = b2-4ac
Δ = 02-4·75·(-686)
Δ = 205800
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:

$\sqrt{\Delta}=\sqrt{205800}=\sqrt{4900*42}=\sqrt{4900}*\sqrt{42}=70\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{42}}{2*75}=\frac{0-70\sqrt{42}}{150}
=-\frac{70\sqrt{42}}{150}
=-\frac{7\sqrt{42}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{42}}{2*75}=\frac{0+70\sqrt{42}}{150}
=\frac{70\sqrt{42}}{150}
=\frac{7\sqrt{42}}{15}
$