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-4x(x+7)+33=9-5x
We move all terms to the left:
-4x(x+7)+33-(9-5x)=0
We add all the numbers together, and all the variables
-4x(x+7)-(-5x+9)+33=0
We multiply parentheses
-4x^2-28x-(-5x+9)+33=0
We get rid of parentheses
-4x^2-28x+5x-9+33=0
We add all the numbers together, and all the variables
-4x^2-23x+24=0
a = -4; b = -23; c = +24;
Δ = b2-4ac
Δ = -232-4·(-4)·24
Δ = 913
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{913}}{2*-4}=\frac{23-\sqrt{913}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{913}}{2*-4}=\frac{23+\sqrt{913}}{-8} $
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