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(3x-7)(x+11)=21+28
We move all terms to the left:
(3x-7)(x+11)-(21+28)=0
We add all the numbers together, and all the variables
(3x-7)(x+11)-49=0
We multiply parentheses ..
(+3x^2+33x-7x-77)-49=0
We get rid of parentheses
3x^2+33x-7x-77-49=0
We add all the numbers together, and all the variables
3x^2+26x-126=0
a = 3; b = 26; c = -126;
Δ = b2-4ac
Δ = 262-4·3·(-126)
Δ = 2188
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2188}=\sqrt{4*547}=\sqrt{4}*\sqrt{547}=2\sqrt{547}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{547}}{2*3}=\frac{-26-2\sqrt{547}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{547}}{2*3}=\frac{-26+2\sqrt{547}}{6} $
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