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(6x-19)(3x+7)=84
We move all terms to the left:
(6x-19)(3x+7)-(84)=0
We multiply parentheses ..
(+18x^2+42x-57x-133)-84=0
We get rid of parentheses
18x^2+42x-57x-133-84=0
We add all the numbers together, and all the variables
18x^2-15x-217=0
a = 18; b = -15; c = -217;
Δ = b2-4ac
Δ = -152-4·18·(-217)
Δ = 15849
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15849}=\sqrt{9*1761}=\sqrt{9}*\sqrt{1761}=3\sqrt{1761}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{1761}}{2*18}=\frac{15-3\sqrt{1761}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{1761}}{2*18}=\frac{15+3\sqrt{1761}}{36} $
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