1500+350x*x=3000+160x*x

Solution for 1500+350x*x=3000+160x*x equation:

1500+350x*x=3000+160x*x

We move all terms to the left:

1500+350x*x-(3000+160x*x)=0

We add all the numbers together, and all the variables

350x*x-(160x*x+3000)+1500=0

Wy multiply elements

350x^2-(160x*x+3000)+1500=0

We get rid of parentheses

350x^2-160x*x-3000+1500=0

We add all the numbers together, and all the variables

350x^2-160x*x-1500=0

Wy multiply elements

350x^2-160x^2-1500=0

We add all the numbers together, and all the variables

190x^2-1500=0

a = 190; b = 0; c = -1500;
Δ = b2-4ac
Δ = 02-4·190·(-1500)
Δ = 1140000
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:

$\sqrt{\Delta}=\sqrt{1140000}=\sqrt{10000*114}=\sqrt{10000}*\sqrt{114}=100\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{114}}{2*190}=\frac{0-100\sqrt{114}}{380}
=-\frac{100\sqrt{114}}{380}
=-\frac{5\sqrt{114}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{114}}{2*190}=\frac{0+100\sqrt{114}}{380}
=\frac{100\sqrt{114}}{380}
=\frac{5\sqrt{114}}{19}
$