.75X^2-6x+20=2.75X+1.5

Solution for .75X^2-6x+20=2.75X+1.5 equation:

.75X^2-6X+20=2.75X+1.5

We move all terms to the left:

.75X^2-6X+20-(2.75X+1.5)=0

We get rid of parentheses

.75X^2-6X-2.75X-1.5+20=0

We add all the numbers together, and all the variables

.75X^2-8.75X+18.5=0

a = .75; b = -8.75; c = +18.5;
Δ = b2-4ac
Δ = -8.752-4·.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*.75}=\frac{8.75-\sqrt{21.0625}}{1.5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.75)+\sqrt{21.0625}}{2*.75}=\frac{8.75+\sqrt{21.0625}}{1.5}
$