5x^2-3x=240-3x

Solution for 5x^2-3x=240-3x equation:

5x^2-3x=240-3x

We move all terms to the left:

5x^2-3x-(240-3x)=0

We add all the numbers together, and all the variables

5x^2-3x-(-3x+240)=0

We get rid of parentheses

5x^2-3x+3x-240=0

We add all the numbers together, and all the variables

5x^2-240=0

a = 5; b = 0; c = -240;
Δ = b2-4ac
Δ = 02-4·5·(-240)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*5}=\frac{0-40\sqrt{3}}{10}
=-\frac{40\sqrt{3}}{10}
=-4\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*5}=\frac{0+40\sqrt{3}}{10}
=\frac{40\sqrt{3}}{10}
=4\sqrt{3}
$