-4x^2+7x+7.5=0

Solution for -4x^2+7x+7.5=0 equation:

-4x^2+7x+7.5=0

a = -4; b = 7; c = +7.5;
Δ = b2-4ac
Δ = 72-4·(-4)·7.5
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-4}=\frac{-20}{-8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-4}=\frac{6}{-8}
=-3/4
$