0.5x^2+0.75x2=4^2

Solution for 0.5x^2+0.75x2=4^2 equation:

0.5x^2+0.75x^2=4^2

We move all terms to the left:

0.5x^2+0.75x^2-(4^2)=0

We add all the numbers together, and all the variables

1.25x^2-16=0

a = 1.25; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·1.25·(-16)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5}}{2*1.25}=\frac{0-4\sqrt{5}}{2.5}
=-\frac{4\sqrt{5}}{2.5}
=-\frac{2\sqrt{5}}{1.25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5}}{2*1.25}=\frac{0+4\sqrt{5}}{2.5}
=\frac{4\sqrt{5}}{2.5}
=\frac{2\sqrt{5}}{1.25}
$