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(6x-19)(3x+7)=180
We move all terms to the left:
(6x-19)(3x+7)-(180)=0
We multiply parentheses ..
(+18x^2+42x-57x-133)-180=0
We get rid of parentheses
18x^2+42x-57x-133-180=0
We add all the numbers together, and all the variables
18x^2-15x-313=0
a = 18; b = -15; c = -313;
Δ = b2-4ac
Δ = -152-4·18·(-313)
Δ = 22761
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{22761}=\sqrt{81*281}=\sqrt{81}*\sqrt{281}=9\sqrt{281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9\sqrt{281}}{2*18}=\frac{15-9\sqrt{281}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9\sqrt{281}}{2*18}=\frac{15+9\sqrt{281}}{36} $
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