175x+175(x+160)=(x)(x+160)

Solution for 175x+175(x+160)=(x)(x+160) equation:

175x+175(x+160)=(x)(x+160)

We move all terms to the left:

175x+175(x+160)-((x)(x+160))=0

We multiply parentheses

175x+175x-(x(x+160))+28000=0


We calculate terms in parentheses: -(x(x+160)), so:

x(x+160)

We multiply parentheses

x^2+160x

Back to the equation:

-(x^2+160x)


We add all the numbers together, and all the variables

350x-(x^2+160x)+28000=0

We get rid of parentheses

-x^2+350x-160x+28000=0

We add all the numbers together, and all the variables

-1x^2+190x+28000=0

a = -1; b = 190; c = +28000;
Δ = b2-4ac
Δ = 1902-4·(-1)·28000
Δ = 148100
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:

$\sqrt{\Delta}=\sqrt{148100}=\sqrt{100*1481}=\sqrt{100}*\sqrt{1481}=10\sqrt{1481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(190)-10\sqrt{1481}}{2*-1}=\frac{-190-10\sqrt{1481}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(190)+10\sqrt{1481}}{2*-1}=\frac{-190+10\sqrt{1481}}{-2}
$