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15xx(6x+3)+7x=40
We move all terms to the left:
15xx(6x+3)+7x-(40)=0
We add all the numbers together, and all the variables
7x+15xx(6x+3)-40=0
We multiply parentheses
90x^2+7x+45x-40=0
We add all the numbers together, and all the variables
90x^2+52x-40=0
a = 90; b = 52; c = -40;
Δ = b2-4ac
Δ = 522-4·90·(-40)
Δ = 17104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{17104}=\sqrt{16*1069}=\sqrt{16}*\sqrt{1069}=4\sqrt{1069}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{1069}}{2*90}=\frac{-52-4\sqrt{1069}}{180} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{1069}}{2*90}=\frac{-52+4\sqrt{1069}}{180} $
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