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3x+5-x^2=5x-8+2x-3
We move all terms to the left:
3x+5-x^2-(5x-8+2x-3)=0
We add all the numbers together, and all the variables
-x^2+3x-(7x-11)+5=0
We add all the numbers together, and all the variables
-1x^2+3x-(7x-11)+5=0
We get rid of parentheses
-1x^2+3x-7x+11+5=0
We add all the numbers together, and all the variables
-1x^2-4x+16=0
a = -1; b = -4; c = +16;
Δ = b2-4ac
Δ = -42-4·(-1)·16
Δ = 80
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{5}}{2*-1}=\frac{4-4\sqrt{5}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{5}}{2*-1}=\frac{4+4\sqrt{5}}{-2} $
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