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(5x+8)2x=71
We move all terms to the left:
(5x+8)2x-(71)=0
We multiply parentheses
10x^2+16x-71=0
a = 10; b = 16; c = -71;
Δ = b2-4ac
Δ = 162-4·10·(-71)
Δ = 3096
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3096}=\sqrt{36*86}=\sqrt{36}*\sqrt{86}=6\sqrt{86}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-6\sqrt{86}}{2*10}=\frac{-16-6\sqrt{86}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+6\sqrt{86}}{2*10}=\frac{-16+6\sqrt{86}}{20} $
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