37=x^2/(4900-70x)

Solution for 37=x^2/(4900-70x) equation:

37=x^2/(4900-70x)

We move all terms to the left:

37-(x^2/(4900-70x))=0


Domain of the equation: (4900-70x))!=0

We move all terms containing x to the left, all other terms to the right

-70x)!=-4900

x!=-4900/1

x!=-4900

x∈R


We add all the numbers together, and all the variables

-(x^2/(-70x+4900))+37=0

We multiply all the terms by the denominator


-(x^2+37*(-70x+4900))=0


We calculate terms in parentheses: -(x^2+37*(-70x+4900)), so:

x^2+37*(-70x+4900)

We multiply parentheses

x^2-2590x+181300

Back to the equation:

-(x^2-2590x+181300)


We get rid of parentheses

-x^2+2590x-181300=0

We add all the numbers together, and all the variables

-1x^2+2590x-181300=0

a = -1; b = 2590; c = -181300;
Δ = b2-4ac
Δ = 25902-4·(-1)·(-181300)
Δ = 5982900
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:

$\sqrt{\Delta}=\sqrt{5982900}=\sqrt{4900*1221}=\sqrt{4900}*\sqrt{1221}=70\sqrt{1221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2590)-70\sqrt{1221}}{2*-1}=\frac{-2590-70\sqrt{1221}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2590)+70\sqrt{1221}}{2*-1}=\frac{-2590+70\sqrt{1221}}{-2}
$