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(6x-19)(3x+7)+84=180
We move all terms to the left:
(6x-19)(3x+7)+84-(180)=0
We add all the numbers together, and all the variables
(6x-19)(3x+7)-96=0
We multiply parentheses ..
(+18x^2+42x-57x-133)-96=0
We get rid of parentheses
18x^2+42x-57x-133-96=0
We add all the numbers together, and all the variables
18x^2-15x-229=0
a = 18; b = -15; c = -229;
Δ = b2-4ac
Δ = -152-4·18·(-229)
Δ = 16713
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16713}=\sqrt{9*1857}=\sqrt{9}*\sqrt{1857}=3\sqrt{1857}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{1857}}{2*18}=\frac{15-3\sqrt{1857}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{1857}}{2*18}=\frac{15+3\sqrt{1857}}{36} $
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