2x^2+5x-75/8=0

Solution for 2x^2+5x-75/8=0 equation:

2x^2+5x-75/8=0

We multiply all the terms by the denominator


2x^2*8+5x*8-75=0

Wy multiply elements

16x^2+40x-75=0

a = 16; b = 40; c = -75;
Δ = b2-4ac
Δ = 402-4·16·(-75)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-80}{2*16}=\frac{-120}{32}
=-3+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+80}{2*16}=\frac{40}{32}
=1+1/4
$