5/3=-15x^2+50x

Solution for 5/3=-15x^2+50x equation:

5/3=-15x^2+50x

We move all terms to the left:

5/3-(-15x^2+50x)=0

We get rid of parentheses

15x^2-50x+5/3=0

We multiply all the terms by the denominator


15x^2*3-50x*3+5=0

Wy multiply elements

45x^2-150x+5=0

a = 45; b = -150; c = +5;
Δ = b2-4ac
Δ = -1502-4·45·5
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-60\sqrt{6}}{2*45}=\frac{150-60\sqrt{6}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+60\sqrt{6}}{2*45}=\frac{150+60\sqrt{6}}{90}
$