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

We get rid of parentheses

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