((12x^2)/5)+2x=300

Solution for ((12x^2)/5)+2x=300 equation:

((12x^2)/5)+2x=300

We move all terms to the left:

((12x^2)/5)+2x-(300)=0

We add all the numbers together, and all the variables

2x+(12x^2/5)-300=0

We get rid of parentheses

12x^2/5+2x-300=0

We multiply all the terms by the denominator


12x^2+2x*5-300*5=0

We add all the numbers together, and all the variables

12x^2+2x*5-1500=0

Wy multiply elements

12x^2+10x-1500=0

a = 12; b = 10; c = -1500;
Δ = b2-4ac
Δ = 102-4·12·(-1500)
Δ = 72100
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:

$\sqrt{\Delta}=\sqrt{72100}=\sqrt{100*721}=\sqrt{100}*\sqrt{721}=10\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{721}}{2*12}=\frac{-10-10\sqrt{721}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{721}}{2*12}=\frac{-10+10\sqrt{721}}{24}
$