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5x(-14-x)=-30-2x
We move all terms to the left:
5x(-14-x)-(-30-2x)=0
We add all the numbers together, and all the variables
5x(-1x-14)-(-2x-30)=0
We multiply parentheses
-5x^2-70x-(-2x-30)=0
We get rid of parentheses
-5x^2-70x+2x+30=0
We add all the numbers together, and all the variables
-5x^2-68x+30=0
a = -5; b = -68; c = +30;
Δ = b2-4ac
Δ = -682-4·(-5)·30
Δ = 5224
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5224}=\sqrt{4*1306}=\sqrt{4}*\sqrt{1306}=2\sqrt{1306}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-2\sqrt{1306}}{2*-5}=\frac{68-2\sqrt{1306}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+2\sqrt{1306}}{2*-5}=\frac{68+2\sqrt{1306}}{-10} $
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