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(5x+4)(x-3)=8
We move all terms to the left:
(5x+4)(x-3)-(8)=0
We multiply parentheses ..
(+5x^2-15x+4x-12)-8=0
We get rid of parentheses
5x^2-15x+4x-12-8=0
We add all the numbers together, and all the variables
5x^2-11x-20=0
a = 5; b = -11; c = -20;
Δ = b2-4ac
Δ = -112-4·5·(-20)
Δ = 521
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{-(-11)-\sqrt{521}}{2*5}=\frac{11-\sqrt{521}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{521}}{2*5}=\frac{11+\sqrt{521}}{10} $
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