975=375+80x+4x^2

Solution for 975=375+80x+4x^2 equation:

975=375+80x+4x^2

We move all terms to the left:

975-(375+80x+4x^2)=0

We get rid of parentheses

-4x^2-80x-375+975=0

We add all the numbers together, and all the variables

-4x^2-80x+600=0

a = -4; b = -80; c = +600;
Δ = b2-4ac
Δ = -802-4·(-4)·600
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-40\sqrt{10}}{2*-4}=\frac{80-40\sqrt{10}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+40\sqrt{10}}{2*-4}=\frac{80+40\sqrt{10}}{-8}
$