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3x^2+5=8-5x
We move all terms to the left:
3x^2+5-(8-5x)=0
We add all the numbers together, and all the variables
3x^2-(-5x+8)+5=0
We get rid of parentheses
3x^2+5x-8+5=0
We add all the numbers together, and all the variables
3x^2+5x-3=0
a = 3; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·3·(-3)
Δ = 61
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{61}}{2*3}=\frac{-5-\sqrt{61}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{61}}{2*3}=\frac{-5+\sqrt{61}}{6} $
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