3.5x^2-3x-4.5=0

Solution for 3.5x^2-3x-4.5=0 equation:

3.5x^2-3x-4.5=0

a = 3.5; b = -3; c = -4.5;
Δ = b2-4ac
Δ = -32-4·3.5·(-4.5)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-6\sqrt{2}}{2*3.5}=\frac{3-6\sqrt{2}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+6\sqrt{2}}{2*3.5}=\frac{3+6\sqrt{2}}{7}
$