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(4x-46)(x+1)=180
We move all terms to the left:
(4x-46)(x+1)-(180)=0
We multiply parentheses ..
(+4x^2+4x-46x-46)-180=0
We get rid of parentheses
4x^2+4x-46x-46-180=0
We add all the numbers together, and all the variables
4x^2-42x-226=0
a = 4; b = -42; c = -226;
Δ = b2-4ac
Δ = -422-4·4·(-226)
Δ = 5380
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5380}=\sqrt{4*1345}=\sqrt{4}*\sqrt{1345}=2\sqrt{1345}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{1345}}{2*4}=\frac{42-2\sqrt{1345}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{1345}}{2*4}=\frac{42+2\sqrt{1345}}{8} $
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