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8x(x+5)=2x-14
We move all terms to the left:
8x(x+5)-(2x-14)=0
We multiply parentheses
8x^2+40x-(2x-14)=0
We get rid of parentheses
8x^2+40x-2x+14=0
We add all the numbers together, and all the variables
8x^2+38x+14=0
a = 8; b = 38; c = +14;
Δ = b2-4ac
Δ = 382-4·8·14
Δ = 996
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{249}}{2*8}=\frac{-38-2\sqrt{249}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{249}}{2*8}=\frac{-38+2\sqrt{249}}{16} $
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