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3x^2+5=5x^2-8x
We move all terms to the left:
3x^2+5-(5x^2-8x)=0
We get rid of parentheses
3x^2-5x^2+8x+5=0
We add all the numbers together, and all the variables
-2x^2+8x+5=0
a = -2; b = 8; c = +5;
Δ = b2-4ac
Δ = 82-4·(-2)·5
Δ = 104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{26}}{2*-2}=\frac{-8-2\sqrt{26}}{-4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{26}}{2*-2}=\frac{-8+2\sqrt{26}}{-4} $
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