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5x^2-6x+2=4x^2+3x+24
We move all terms to the left:
5x^2-6x+2-(4x^2+3x+24)=0
We get rid of parentheses
5x^2-4x^2-6x-3x-24+2=0
We add all the numbers together, and all the variables
x^2-9x-22=0
a = 1; b = -9; c = -22;
Δ = b2-4ac
Δ = -92-4·1·(-22)
Δ = 169
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-13}{2*1}=\frac{-4}{2} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+13}{2*1}=\frac{22}{2} =11 $
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