302=4x-2500/3x-2500

Solution for 302=4x-2500/3x-2500 equation:

302=4x-2500/3x-2500

We move all terms to the left:

302-(4x-2500/3x-2500)=0


Domain of the equation: 3x-2500)!=0

x∈R


We get rid of parentheses

-4x+2500/3x+2500+302=0

We multiply all the terms by the denominator


-4x*3x+2500*3x+302*3x+2500=0

Wy multiply elements

-12x^2+7500x+906x+2500=0

We add all the numbers together, and all the variables

-12x^2+8406x+2500=0

a = -12; b = 8406; c = +2500;
Δ = b2-4ac
Δ = 84062-4·(-12)·2500
Δ = 70780836
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:

$\sqrt{\Delta}=\sqrt{70780836}=\sqrt{4*17695209}=\sqrt{4}*\sqrt{17695209}=2\sqrt{17695209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8406)-2\sqrt{17695209}}{2*-12}=\frac{-8406-2\sqrt{17695209}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8406)+2\sqrt{17695209}}{2*-12}=\frac{-8406+2\sqrt{17695209}}{-24}
$