0.75x^2-3x=5

Solution for 0.75x^2-3x=5 equation:

0.75x^2-3x=5

We move all terms to the left:

0.75x^2-3x-(5)=0

a = 0.75; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·0.75·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-2\sqrt{6}}{2*0.75}=\frac{3-2\sqrt{6}}{1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+2\sqrt{6}}{2*0.75}=\frac{3+2\sqrt{6}}{1.5}
$