2x^2-x-100/75=0

Solution for 2x^2-x-100/75=0 equation:

2x^2-x-100/75=0

We add all the numbers together, and all the variables

2x^2-1x-100/75=0

We multiply all the terms by the denominator


2x^2*75-1x*75-100=0

Wy multiply elements

150x^2-75x-100=0

a = 150; b = -75; c = -100;
Δ = b2-4ac
Δ = -752-4·150·(-100)
Δ = 65625
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:

$\sqrt{\Delta}=\sqrt{65625}=\sqrt{625*105}=\sqrt{625}*\sqrt{105}=25\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-25\sqrt{105}}{2*150}=\frac{75-25\sqrt{105}}{300}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+25\sqrt{105}}{2*150}=\frac{75+25\sqrt{105}}{300}
$