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4x^2+6x-9=11-5x
We move all terms to the left:
4x^2+6x-9-(11-5x)=0
We add all the numbers together, and all the variables
4x^2+6x-(-5x+11)-9=0
We get rid of parentheses
4x^2+6x+5x-11-9=0
We add all the numbers together, and all the variables
4x^2+11x-20=0
a = 4; b = 11; c = -20;
Δ = b2-4ac
Δ = 112-4·4·(-20)
Δ = 441
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{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*4}=\frac{-32}{8} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*4}=\frac{10}{8} =1+1/4 $
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