(4x^2+5x)/3=67500

Solution for (4x^2+5x)/3=67500 equation:

(4x^2+5x)/3=67500

We move all terms to the left:

(4x^2+5x)/3-(67500)=0

We multiply all the terms by the denominator


(4x^2+5x)-67500*3=0

We add all the numbers together, and all the variables

(4x^2+5x)-202500=0

We get rid of parentheses

4x^2+5x-202500=0

a = 4; b = 5; c = -202500;
Δ = b2-4ac
Δ = 52-4·4·(-202500)
Δ = 3240025
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:

$\sqrt{\Delta}=\sqrt{3240025}=\sqrt{25*129601}=\sqrt{25}*\sqrt{129601}=5\sqrt{129601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{129601}}{2*4}=\frac{-5-5\sqrt{129601}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{129601}}{2*4}=\frac{-5+5\sqrt{129601}}{8}
$