2x^2+15X-4.5=0

Solution for 2x^2+15X-4.5=0 equation:

2x^2+15x-4.5=0

a = 2; b = 15; c = -4.5;
Δ = b2-4ac
Δ = 152-4·2·(-4.5)
Δ = 261
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:

$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{29}}{2*2}=\frac{-15-3\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{29}}{2*2}=\frac{-15+3\sqrt{29}}{4}
$