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(3x+14)(7x-4)=180
We move all terms to the left:
(3x+14)(7x-4)-(180)=0
We multiply parentheses ..
(+21x^2-12x+98x-56)-180=0
We get rid of parentheses
21x^2-12x+98x-56-180=0
We add all the numbers together, and all the variables
21x^2+86x-236=0
a = 21; b = 86; c = -236;
Δ = b2-4ac
Δ = 862-4·21·(-236)
Δ = 27220
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{27220}=\sqrt{4*6805}=\sqrt{4}*\sqrt{6805}=2\sqrt{6805}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-2\sqrt{6805}}{2*21}=\frac{-86-2\sqrt{6805}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+2\sqrt{6805}}{2*21}=\frac{-86+2\sqrt{6805}}{42} $
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