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2x(x-3)=6x+5
We move all terms to the left:
2x(x-3)-(6x+5)=0
We multiply parentheses
2x^2-6x-(6x+5)=0
We get rid of parentheses
2x^2-6x-6x-5=0
We add all the numbers together, and all the variables
2x^2-12x-5=0
a = 2; b = -12; c = -5;
Δ = b2-4ac
Δ = -122-4·2·(-5)
Δ = 184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{46}}{2*2}=\frac{12-2\sqrt{46}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{46}}{2*2}=\frac{12+2\sqrt{46}}{4} $
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