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8x(-21+5x)=-15
We move all terms to the left:
8x(-21+5x)-(-15)=0
We add all the numbers together, and all the variables
8x(5x-21)-(-15)=0
We add all the numbers together, and all the variables
8x(5x-21)+15=0
We multiply parentheses
40x^2-168x+15=0
a = 40; b = -168; c = +15;
Δ = b2-4ac
Δ = -1682-4·40·15
Δ = 25824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25824}=\sqrt{16*1614}=\sqrt{16}*\sqrt{1614}=4\sqrt{1614}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-4\sqrt{1614}}{2*40}=\frac{168-4\sqrt{1614}}{80} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+4\sqrt{1614}}{2*40}=\frac{168+4\sqrt{1614}}{80} $
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