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(2x-3)2x=30
We move all terms to the left:
(2x-3)2x-(30)=0
We multiply parentheses
4x^2-6x-30=0
a = 4; b = -6; c = -30;
Δ = b2-4ac
Δ = -62-4·4·(-30)
Δ = 516
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{129}}{2*4}=\frac{6-2\sqrt{129}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{129}}{2*4}=\frac{6+2\sqrt{129}}{8} $
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