237x-7x^2=220+25x

Solution for 237x-7x^2=220+25x equation:

237x-7x^2=220+25x

We move all terms to the left:

237x-7x^2-(220+25x)=0

We add all the numbers together, and all the variables

-7x^2+237x-(25x+220)=0

We get rid of parentheses

-7x^2+237x-25x-220=0

We add all the numbers together, and all the variables

-7x^2+212x-220=0

a = -7; b = 212; c = -220;
Δ = b2-4ac
Δ = 2122-4·(-7)·(-220)
Δ = 38784
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:

$\sqrt{\Delta}=\sqrt{38784}=\sqrt{64*606}=\sqrt{64}*\sqrt{606}=8\sqrt{606}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(212)-8\sqrt{606}}{2*-7}=\frac{-212-8\sqrt{606}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(212)+8\sqrt{606}}{2*-7}=\frac{-212+8\sqrt{606}}{-14}
$