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(2x+46)(x-6)=180
We move all terms to the left:
(2x+46)(x-6)-(180)=0
We multiply parentheses ..
(+2x^2-12x+46x-276)-180=0
We get rid of parentheses
2x^2-12x+46x-276-180=0
We add all the numbers together, and all the variables
2x^2+34x-456=0
a = 2; b = 34; c = -456;
Δ = b2-4ac
Δ = 342-4·2·(-456)
Δ = 4804
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4804}=\sqrt{4*1201}=\sqrt{4}*\sqrt{1201}=2\sqrt{1201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{1201}}{2*2}=\frac{-34-2\sqrt{1201}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{1201}}{2*2}=\frac{-34+2\sqrt{1201}}{4} $
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