-4u(-5u+7)-8u=3(u-3)-7

Solution for -4u(-5u+7)-8u=3(u-3)-7 equation:

-4u(-5u+7)-8u=3(u-3)-7

We move all terms to the left:

-4u(-5u+7)-8u-(3(u-3)-7)=0

We add all the numbers together, and all the variables

-8u-4u(-5u+7)-(3(u-3)-7)=0

We multiply parentheses

20u^2-8u-28u-(3(u-3)-7)=0


We calculate terms in parentheses: -(3(u-3)-7), so:

3(u-3)-7

We multiply parentheses

3u-9-7

We add all the numbers together, and all the variables

3u-16

Back to the equation:

-(3u-16)


We add all the numbers together, and all the variables

20u^2-36u-(3u-16)=0

We get rid of parentheses

20u^2-36u-3u+16=0

We add all the numbers together, and all the variables

20u^2-39u+16=0

a = 20; b = -39; c = +16;
Δ = b2-4ac
Δ = -392-4·20·16
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{241}}{2*20}=\frac{39-\sqrt{241}}{40}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{241}}{2*20}=\frac{39+\sqrt{241}}{40}
$