7.50+x(2.00+x)=83.00x

Solution for 7.50+x(2.00+x)=83.00x equation:

7.50+x(2.00+x)=83.00x

We move all terms to the left:

7.50+x(2.00+x)-(83.00x)=0

We add all the numbers together, and all the variables

x(x+2)-(+83.00x)+7.50=0

We add all the numbers together, and all the variables

x(x+2)-(+83.00x)+7.5=0

We multiply parentheses

x^2+2x-(+83.00x)+7.5=0

We get rid of parentheses

x^2+2x-83.00x+7.5=0

We add all the numbers together, and all the variables

x^2-81x+7.5=0

a = 1; b = -81; c = +7.5;
Δ = b2-4ac
Δ = -812-4·1·7.5
Δ = 6531
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{-(-81)-\sqrt{6531}}{2*1}=\frac{81-\sqrt{6531}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{6531}}{2*1}=\frac{81+\sqrt{6531}}{2}
$