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5x(2x+4)=34
We move all terms to the left:
5x(2x+4)-(34)=0
We multiply parentheses
10x^2+20x-34=0
a = 10; b = 20; c = -34;
Δ = b2-4ac
Δ = 202-4·10·(-34)
Δ = 1760
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1760}=\sqrt{16*110}=\sqrt{16}*\sqrt{110}=4\sqrt{110}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{110}}{2*10}=\frac{-20-4\sqrt{110}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{110}}{2*10}=\frac{-20+4\sqrt{110}}{20} $
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