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5x(2x-4)=4+6x
We move all terms to the left:
5x(2x-4)-(4+6x)=0
We add all the numbers together, and all the variables
5x(2x-4)-(6x+4)=0
We multiply parentheses
10x^2-20x-(6x+4)=0
We get rid of parentheses
10x^2-20x-6x-4=0
We add all the numbers together, and all the variables
10x^2-26x-4=0
a = 10; b = -26; c = -4;
Δ = b2-4ac
Δ = -262-4·10·(-4)
Δ = 836
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{209}}{2*10}=\frac{26-2\sqrt{209}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{209}}{2*10}=\frac{26+2\sqrt{209}}{20} $
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