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(3x+19)(7x+5)+(2x+8)=180
We move all terms to the left:
(3x+19)(7x+5)+(2x+8)-(180)=0
We get rid of parentheses
(3x+19)(7x+5)+2x+8-180=0
We multiply parentheses ..
(+21x^2+15x+133x+95)+2x+8-180=0
We add all the numbers together, and all the variables
(+21x^2+15x+133x+95)+2x-172=0
We get rid of parentheses
21x^2+15x+133x+2x+95-172=0
We add all the numbers together, and all the variables
21x^2+150x-77=0
a = 21; b = 150; c = -77;
Δ = b2-4ac
Δ = 1502-4·21·(-77)
Δ = 28968
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28968}=\sqrt{4*7242}=\sqrt{4}*\sqrt{7242}=2\sqrt{7242}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{7242}}{2*21}=\frac{-150-2\sqrt{7242}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{7242}}{2*21}=\frac{-150+2\sqrt{7242}}{42} $
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