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-14+(4x+7)x=5
We move all terms to the left:
-14+(4x+7)x-(5)=0
We add all the numbers together, and all the variables
(4x+7)x-19=0
We multiply parentheses
4x^2+7x-19=0
a = 4; b = 7; c = -19;
Δ = b2-4ac
Δ = 72-4·4·(-19)
Δ = 353
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{-(7)-\sqrt{353}}{2*4}=\frac{-7-\sqrt{353}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{353}}{2*4}=\frac{-7+\sqrt{353}}{8} $
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