(x+1)(x+.75)=31.50

Solution for (x+1)(x+.75)=31.50 equation:

(x+1)(x+.75)=31.50

We move all terms to the left:

(x+1)(x+.75)-(31.50)=0

We add all the numbers together, and all the variables

(x+1)(x+0.75)-(31.5)=0

We add all the numbers together, and all the variables

(x+1)(x+0.75)-31.5=0

We multiply parentheses ..

(+x^2+0.75x+x+0.75)-31.5=0

We get rid of parentheses

x^2+0.75x+x+0.75-31.5=0

We add all the numbers together, and all the variables

x^2+1.75x-30.75=0

a = 1; b = 1.75; c = -30.75;
Δ = b2-4ac
Δ = 1.752-4·1·(-30.75)
Δ = 126.0625
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{-(1.75)-\sqrt{126.0625}}{2*1}=\frac{-1.75-\sqrt{126.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.75)+\sqrt{126.0625}}{2*1}=\frac{-1.75+\sqrt{126.0625}}{2}
$