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3x+5-x^2=5x-8+2x
We move all terms to the left:
3x+5-x^2-(5x-8+2x)=0
We add all the numbers together, and all the variables
-x^2+3x-(7x-8)+5=0
We add all the numbers together, and all the variables
-1x^2+3x-(7x-8)+5=0
We get rid of parentheses
-1x^2+3x-7x+8+5=0
We add all the numbers together, and all the variables
-1x^2-4x+13=0
a = -1; b = -4; c = +13;
Δ = b2-4ac
Δ = -42-4·(-1)·13
Δ = 68
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{17}}{2*-1}=\frac{4-2\sqrt{17}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{17}}{2*-1}=\frac{4+2\sqrt{17}}{-2} $
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