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-2x(3x-13)=4x-24
We move all terms to the left:
-2x(3x-13)-(4x-24)=0
We multiply parentheses
-6x^2+26x-(4x-24)=0
We get rid of parentheses
-6x^2+26x-4x+24=0
We add all the numbers together, and all the variables
-6x^2+22x+24=0
a = -6; b = 22; c = +24;
Δ = b2-4ac
Δ = 222-4·(-6)·24
Δ = 1060
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{265}}{2*-6}=\frac{-22-2\sqrt{265}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{265}}{2*-6}=\frac{-22+2\sqrt{265}}{-12} $
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