0.75x^2-6x+20=2.75x+1.50

Solution for 0.75x^2-6x+20=2.75x+1.50 equation:

0.75x^2-6x+20=2.75x+1.50

We move all terms to the left:

0.75x^2-6x+20-(2.75x+1.50)=0

We add all the numbers together, and all the variables

0.75x^2-6x-(2.75x+1.5)+20=0

We get rid of parentheses

0.75x^2-6x-2.75x-1.5+20=0

We add all the numbers together, and all the variables

0.75x^2-8.75x+18.5=0

a = 0.75; b = -8.75; c = +18.5;
Δ = b2-4ac
Δ = -8.752-4·0.75·18.5
Δ = 21.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8.75)-\sqrt{21.0625}}{2*0.75}=\frac{8.75-\sqrt{21.0625}}{1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.75)+\sqrt{21.0625}}{2*0.75}=\frac{8.75+\sqrt{21.0625}}{1.5}
$