4x^2+42x=72

Solution for 4x^2+42x=72 equation:

4x^2+42x=72

We move all terms to the left:

4x^2+42x-(72)=0

a = 4; b = 42; c = -72;
Δ = b2-4ac
Δ = 422-4·4·(-72)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-54}{2*4}=\frac{-96}{8}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+54}{2*4}=\frac{12}{8}
=1+1/2
$