x2-5=1+1.5x

Solution for x2-5=1+1.5x equation:

x2-5=1+1.5x

We move all terms to the left:

x2-5-(1+1.5x)=0

We add all the numbers together, and all the variables

x2-(1.5x+1)-5=0

We add all the numbers together, and all the variables

x^2-(1.5x+1)-5=0

We get rid of parentheses

x^2-1.5x-1-5=0

We add all the numbers together, and all the variables

x^2-1.5x-6=0

a = 1; b = -1.5; c = -6;
Δ = b2-4ac
Δ = -1.52-4·1·(-6)
Δ = 26.25
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{-(-1.5)-\sqrt{26.25}}{2*1}=\frac{1.5-\sqrt{26.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{26.25}}{2*1}=\frac{1.5+\sqrt{26.25}}{2}
$