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12+5x(2x+7)=90
We move all terms to the left:
12+5x(2x+7)-(90)=0
We add all the numbers together, and all the variables
5x(2x+7)-78=0
We multiply parentheses
10x^2+35x-78=0
a = 10; b = 35; c = -78;
Δ = b2-4ac
Δ = 352-4·10·(-78)
Δ = 4345
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{-(35)-\sqrt{4345}}{2*10}=\frac{-35-\sqrt{4345}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{4345}}{2*10}=\frac{-35+\sqrt{4345}}{20} $
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