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(2x-14)(3x+2)=180
We move all terms to the left:
(2x-14)(3x+2)-(180)=0
We multiply parentheses ..
(+6x^2+4x-42x-28)-180=0
We get rid of parentheses
6x^2+4x-42x-28-180=0
We add all the numbers together, and all the variables
6x^2-38x-208=0
a = 6; b = -38; c = -208;
Δ = b2-4ac
Δ = -382-4·6·(-208)
Δ = 6436
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6436}=\sqrt{4*1609}=\sqrt{4}*\sqrt{1609}=2\sqrt{1609}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{1609}}{2*6}=\frac{38-2\sqrt{1609}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{1609}}{2*6}=\frac{38+2\sqrt{1609}}{12} $
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