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(20-2x)(25-7x)=375
We move all terms to the left:
(20-2x)(25-7x)-(375)=0
We add all the numbers together, and all the variables
(-2x+20)(-7x+25)-375=0
We multiply parentheses ..
(+14x^2-50x-140x+500)-375=0
We get rid of parentheses
14x^2-50x-140x+500-375=0
We add all the numbers together, and all the variables
14x^2-190x+125=0
a = 14; b = -190; c = +125;
Δ = b2-4ac
Δ = -1902-4·14·125
Δ = 29100
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{29100}=\sqrt{100*291}=\sqrt{100}*\sqrt{291}=10\sqrt{291}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-10\sqrt{291}}{2*14}=\frac{190-10\sqrt{291}}{28} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+10\sqrt{291}}{2*14}=\frac{190+10\sqrt{291}}{28} $
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