(8/15)q^2-100q+Y=0

Solution for (8/15)q^2-100q+Y=0 equation:

(8/15)q^2-100q+=0


Domain of the equation: 15)q^2!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

(+8/15)q^2-100q+=0

We add all the numbers together, and all the variables

-100q+(+8/15)q^2=0

We multiply all the terms by the denominator


-100q*15)q^2+(+8=0

Wy multiply elements

-1500q^2+8=0

a = -1500; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-1500)·8
Δ = 48000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48000}=\sqrt{1600*30}=\sqrt{1600}*\sqrt{30}=40\sqrt{30}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{30}}{2*-1500}=\frac{0-40\sqrt{30}}{-3000}
=-\frac{40\sqrt{30}}{-3000}
=-\frac{\sqrt{30}}{-75}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{30}}{2*-1500}=\frac{0+40\sqrt{30}}{-3000}
=\frac{40\sqrt{30}}{-3000}
=\frac{\sqrt{30}}{-75}
$