(2x-3)(7-5x)=-21

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Solution for (2x-3)(7-5x)=-21 equation:



(2x-3)(7-5x)=-21
We move all terms to the left:
(2x-3)(7-5x)-(-21)=0
We add all the numbers together, and all the variables
(2x-3)(-5x+7)-(-21)=0
We add all the numbers together, and all the variables
(2x-3)(-5x+7)+21=0
We multiply parentheses ..
(-10x^2+14x+15x-21)+21=0
We get rid of parentheses
-10x^2+14x+15x-21+21=0
We add all the numbers together, and all the variables
-10x^2+29x=0
a = -10; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-10)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-10}=\frac{-58}{-20} =2+9/10 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-10}=\frac{0}{-20} =0 $

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