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-5x(20+3x)=19
We move all terms to the left:
-5x(20+3x)-(19)=0
We add all the numbers together, and all the variables
-5x(3x+20)-19=0
We multiply parentheses
-15x^2-100x-19=0
a = -15; b = -100; c = -19;
Δ = b2-4ac
Δ = -1002-4·(-15)·(-19)
Δ = 8860
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8860}=\sqrt{4*2215}=\sqrt{4}*\sqrt{2215}=2\sqrt{2215}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2215}}{2*-15}=\frac{100-2\sqrt{2215}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2215}}{2*-15}=\frac{100+2\sqrt{2215}}{-30} $
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