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(2x+14)(4x-2)=5x+1
We move all terms to the left:
(2x+14)(4x-2)-(5x+1)=0
We get rid of parentheses
(2x+14)(4x-2)-5x-1=0
We multiply parentheses ..
(+8x^2-4x+56x-28)-5x-1=0
We get rid of parentheses
8x^2-4x+56x-5x-28-1=0
We add all the numbers together, and all the variables
8x^2+47x-29=0
a = 8; b = 47; c = -29;
Δ = b2-4ac
Δ = 472-4·8·(-29)
Δ = 3137
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{-(47)-\sqrt{3137}}{2*8}=\frac{-47-\sqrt{3137}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+\sqrt{3137}}{2*8}=\frac{-47+\sqrt{3137}}{16} $
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