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3x-4x-8=03-19x^2-14x=0
We move all terms to the left:
3x-4x-8-(03-19x^2-14x)=0
We add all the numbers together, and all the variables
-(03-19x^2-14x)-1x-8=0
We get rid of parentheses
19x^2+14x-1x-03-8=0
We add all the numbers together, and all the variables
19x^2+13x-11=0
a = 19; b = 13; c = -11;
Δ = b2-4ac
Δ = 132-4·19·(-11)
Δ = 1005
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{-(13)-\sqrt{1005}}{2*19}=\frac{-13-\sqrt{1005}}{38} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{1005}}{2*19}=\frac{-13+\sqrt{1005}}{38} $
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