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4x(5x+3)=14x+30
We move all terms to the left:
4x(5x+3)-(14x+30)=0
We multiply parentheses
20x^2+12x-(14x+30)=0
We get rid of parentheses
20x^2+12x-14x-30=0
We add all the numbers together, and all the variables
20x^2-2x-30=0
a = 20; b = -2; c = -30;
Δ = b2-4ac
Δ = -22-4·20·(-30)
Δ = 2404
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2404}=\sqrt{4*601}=\sqrt{4}*\sqrt{601}=2\sqrt{601}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{601}}{2*20}=\frac{2-2\sqrt{601}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{601}}{2*20}=\frac{2+2\sqrt{601}}{40} $
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