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(5x+3)(x-6)=7
We move all terms to the left:
(5x+3)(x-6)-(7)=0
We multiply parentheses ..
(+5x^2-30x+3x-18)-7=0
We get rid of parentheses
5x^2-30x+3x-18-7=0
We add all the numbers together, and all the variables
5x^2-27x-25=0
a = 5; b = -27; c = -25;
Δ = b2-4ac
Δ = -272-4·5·(-25)
Δ = 1229
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{-(-27)-\sqrt{1229}}{2*5}=\frac{27-\sqrt{1229}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1229}}{2*5}=\frac{27+\sqrt{1229}}{10} $
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