7.5x^2+4x-90=0

Solution for 7.5x^2+4x-90=0 equation:

7.5x^2+4x-90=0

a = 7.5; b = 4; c = -90;
Δ = b2-4ac
Δ = 42-4·7.5·(-90)
Δ = 2716
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:

$\sqrt{\Delta}=\sqrt{2716}=\sqrt{4*679}=\sqrt{4}*\sqrt{679}=2\sqrt{679}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{679}}{2*7.5}=\frac{-4-2\sqrt{679}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{679}}{2*7.5}=\frac{-4+2\sqrt{679}}{15}
$