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(x+3)(3x+5)=77
We move all terms to the left:
(x+3)(3x+5)-(77)=0
We multiply parentheses ..
(+3x^2+5x+9x+15)-77=0
We get rid of parentheses
3x^2+5x+9x+15-77=0
We add all the numbers together, and all the variables
3x^2+14x-62=0
a = 3; b = 14; c = -62;
Δ = b2-4ac
Δ = 142-4·3·(-62)
Δ = 940
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{235}}{2*3}=\frac{-14-2\sqrt{235}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{235}}{2*3}=\frac{-14+2\sqrt{235}}{6} $
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