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(10x+3)(8x+19)=90
We move all terms to the left:
(10x+3)(8x+19)-(90)=0
We multiply parentheses ..
(+80x^2+190x+24x+57)-90=0
We get rid of parentheses
80x^2+190x+24x+57-90=0
We add all the numbers together, and all the variables
80x^2+214x-33=0
a = 80; b = 214; c = -33;
Δ = b2-4ac
Δ = 2142-4·80·(-33)
Δ = 56356
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{56356}=\sqrt{4*14089}=\sqrt{4}*\sqrt{14089}=2\sqrt{14089}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(214)-2\sqrt{14089}}{2*80}=\frac{-214-2\sqrt{14089}}{160} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(214)+2\sqrt{14089}}{2*80}=\frac{-214+2\sqrt{14089}}{160} $
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