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3x(x-1)+8(x-3)=6x+7-5x
We move all terms to the left:
3x(x-1)+8(x-3)-(6x+7-5x)=0
We add all the numbers together, and all the variables
3x(x-1)+8(x-3)-(x+7)=0
We multiply parentheses
3x^2-3x+8x-(x+7)-24=0
We get rid of parentheses
3x^2-3x+8x-x-7-24=0
We add all the numbers together, and all the variables
3x^2+4x-31=0
a = 3; b = 4; c = -31;
Δ = b2-4ac
Δ = 42-4·3·(-31)
Δ = 388
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{97}}{2*3}=\frac{-4-2\sqrt{97}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{97}}{2*3}=\frac{-4+2\sqrt{97}}{6} $
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