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(3x+4)(3x-7)=360
We move all terms to the left:
(3x+4)(3x-7)-(360)=0
We multiply parentheses ..
(+9x^2-21x+12x-28)-360=0
We get rid of parentheses
9x^2-21x+12x-28-360=0
We add all the numbers together, and all the variables
9x^2-9x-388=0
a = 9; b = -9; c = -388;
Δ = b2-4ac
Δ = -92-4·9·(-388)
Δ = 14049
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14049}=\sqrt{9*1561}=\sqrt{9}*\sqrt{1561}=3\sqrt{1561}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{1561}}{2*9}=\frac{9-3\sqrt{1561}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{1561}}{2*9}=\frac{9+3\sqrt{1561}}{18} $
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