X^2-7.5x=1.5

Solution for X^2-7.5x=1.5 equation:

X^2-7.5X=1.5

We move all terms to the left:

X^2-7.5X-(1.5)=0

We add all the numbers together, and all the variables

X^2-7.5X-1.5=0

a = 1; b = -7.5; c = -1.5;
Δ = b2-4ac
Δ = -7.52-4·1·(-1.5)
Δ = 62.25
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{-(-7.5)-\sqrt{62.25}}{2*1}=\frac{7.5-\sqrt{62.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{62.25}}{2*1}=\frac{7.5+\sqrt{62.25}}{2}
$