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(2x+9)(6x+4)=37
We move all terms to the left:
(2x+9)(6x+4)-(37)=0
We multiply parentheses ..
(+12x^2+8x+54x+36)-37=0
We get rid of parentheses
12x^2+8x+54x+36-37=0
We add all the numbers together, and all the variables
12x^2+62x-1=0
a = 12; b = 62; c = -1;
Δ = b2-4ac
Δ = 622-4·12·(-1)
Δ = 3892
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3892}=\sqrt{4*973}=\sqrt{4}*\sqrt{973}=2\sqrt{973}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{973}}{2*12}=\frac{-62-2\sqrt{973}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{973}}{2*12}=\frac{-62+2\sqrt{973}}{24} $
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