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7x^2-12x-37=44
We move all terms to the left:
7x^2-12x-37-(44)=0
We add all the numbers together, and all the variables
7x^2-12x-81=0
a = 7; b = -12; c = -81;
Δ = b2-4ac
Δ = -122-4·7·(-81)
Δ = 2412
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2412}=\sqrt{36*67}=\sqrt{36}*\sqrt{67}=6\sqrt{67}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{67}}{2*7}=\frac{12-6\sqrt{67}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{67}}{2*7}=\frac{12+6\sqrt{67}}{14} $
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