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3x(x+3)=8x-5x+7
We move all terms to the left:
3x(x+3)-(8x-5x+7)=0
We add all the numbers together, and all the variables
3x(x+3)-(3x+7)=0
We multiply parentheses
3x^2+9x-(3x+7)=0
We get rid of parentheses
3x^2+9x-3x-7=0
We add all the numbers together, and all the variables
3x^2+6x-7=0
a = 3; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·3·(-7)
Δ = 120
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{30}}{2*3}=\frac{-6-2\sqrt{30}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{30}}{2*3}=\frac{-6+2\sqrt{30}}{6} $
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