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(8x+14)(12x-50)=180
We move all terms to the left:
(8x+14)(12x-50)-(180)=0
We multiply parentheses ..
(+96x^2-400x+168x-700)-180=0
We get rid of parentheses
96x^2-400x+168x-700-180=0
We add all the numbers together, and all the variables
96x^2-232x-880=0
a = 96; b = -232; c = -880;
Δ = b2-4ac
Δ = -2322-4·96·(-880)
Δ = 391744
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{391744}=\sqrt{64*6121}=\sqrt{64}*\sqrt{6121}=8\sqrt{6121}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-8\sqrt{6121}}{2*96}=\frac{232-8\sqrt{6121}}{192} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+8\sqrt{6121}}{2*96}=\frac{232+8\sqrt{6121}}{192} $
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