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5x^2+33x+13=8x-7
We move all terms to the left:
5x^2+33x+13-(8x-7)=0
We get rid of parentheses
5x^2+33x-8x+7+13=0
We add all the numbers together, and all the variables
5x^2+25x+20=0
a = 5; b = 25; c = +20;
Δ = b2-4ac
Δ = 252-4·5·20
Δ = 225
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{225}=15$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-15}{2*5}=\frac{-40}{10} =-4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+15}{2*5}=\frac{-10}{10} =-1 $
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