4x^2+28x=-45

Solution for 4x^2+28x=-45 equation:

4x^2+28x=-45

We move all terms to the left:

4x^2+28x-(-45)=0

We add all the numbers together, and all the variables

4x^2+28x+45=0

a = 4; b = 28; c = +45;
Δ = b2-4ac
Δ = 282-4·4·45
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{-(28)-8}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8}{2*4}=\frac{-20}{8}
=-2+1/2
$