28x^2/15+112x=500

Solution for 28x^2/15+112x=500 equation:

28x^2/15+112x=500

We move all terms to the left:

28x^2/15+112x-(500)=0

We multiply all the terms by the denominator


28x^2+112x*15-500*15=0

We add all the numbers together, and all the variables

28x^2+112x*15-7500=0

Wy multiply elements

28x^2+1680x-7500=0

a = 28; b = 1680; c = -7500;
Δ = b2-4ac
Δ = 16802-4·28·(-7500)
Δ = 3662400
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:

$\sqrt{\Delta}=\sqrt{3662400}=\sqrt{1600*2289}=\sqrt{1600}*\sqrt{2289}=40\sqrt{2289}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1680)-40\sqrt{2289}}{2*28}=\frac{-1680-40\sqrt{2289}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1680)+40\sqrt{2289}}{2*28}=\frac{-1680+40\sqrt{2289}}{56}
$