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14(x.x)-(2x-3)(7x+4)=14
We move all terms to the left:
14(x.x)-(2x-3)(7x+4)-(14)=0
We add all the numbers together, and all the variables
14(+x.x)-(2x-3)(7x+4)-14=0
We multiply parentheses
14x-(2x-3)(7x+4)-14=0
We multiply parentheses ..
-(+14x^2+8x-21x-12)+14x-14=0
We get rid of parentheses
-14x^2-8x+21x+14x+12-14=0
We add all the numbers together, and all the variables
-14x^2+27x-2=0
a = -14; b = 27; c = -2;
Δ = b2-4ac
Δ = 272-4·(-14)·(-2)
Δ = 617
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{617}}{2*-14}=\frac{-27-\sqrt{617}}{-28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{617}}{2*-14}=\frac{-27+\sqrt{617}}{-28} $
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