x^2+7x=3.75

Solution for x^2+7x=3.75 equation:

x^2+7x=3.75

We move all terms to the left:

x^2+7x-(3.75)=0

We add all the numbers together, and all the variables

x^2+7x-3.75=0

a = 1; b = 7; c = -3.75;
Δ = b2-4ac
Δ = 72-4·1·(-3.75)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-8}{2*1}=\frac{-15}{2}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+8}{2*1}=\frac{1}{2}
=1/2
$