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5x(2x+4)-7=0
We multiply parentheses
10x^2+20x-7=0
a = 10; b = 20; c = -7;
Δ = b2-4ac
Δ = 202-4·10·(-7)
Δ = 680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{170}}{2*10}=\frac{-20-2\sqrt{170}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{170}}{2*10}=\frac{-20+2\sqrt{170}}{20} $
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