7x2-75=200

Solution for 7x2-75=200 equation:

7x^2-75=200

We move all terms to the left:

7x^2-75-(200)=0

We add all the numbers together, and all the variables

7x^2-275=0

a = 7; b = 0; c = -275;
Δ = b2-4ac
Δ = 02-4·7·(-275)
Δ = 7700
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:

$\sqrt{\Delta}=\sqrt{7700}=\sqrt{100*77}=\sqrt{100}*\sqrt{77}=10\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{77}}{2*7}=\frac{0-10\sqrt{77}}{14}
=-\frac{10\sqrt{77}}{14}
=-\frac{5\sqrt{77}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{77}}{2*7}=\frac{0+10\sqrt{77}}{14}
=\frac{10\sqrt{77}}{14}
=\frac{5\sqrt{77}}{7}
$