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2x(3-4x)=-8
We move all terms to the left:
2x(3-4x)-(-8)=0
We add all the numbers together, and all the variables
2x(-4x+3)-(-8)=0
We add all the numbers together, and all the variables
2x(-4x+3)+8=0
We multiply parentheses
-8x^2+6x+8=0
a = -8; b = 6; c = +8;
Δ = b2-4ac
Δ = 62-4·(-8)·8
Δ = 292
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{73}}{2*-8}=\frac{-6-2\sqrt{73}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{73}}{2*-8}=\frac{-6+2\sqrt{73}}{-16} $
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