7.5=x^2+7x

Solution for 7.5=x^2+7x equation:

7.5=x^2+7x

We move all terms to the left:

7.5-(x^2+7x)=0

We get rid of parentheses

-x^2-7x+7.5=0

We add all the numbers together, and all the variables

-1x^2-7x+7.5=0

a = -1; b = -7; c = +7.5;
Δ = b2-4ac
Δ = -72-4·(-1)·7.5
Δ = 79
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)-\sqrt{79}}{2*-1}=\frac{7-\sqrt{79}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{79}}{2*-1}=\frac{7+\sqrt{79}}{-2}
$