100(6x+7)=10(x2+16x-7)

Solution for 100(6x+7)=10(x2+16x-7) equation:

100(6x+7)=10(x2+16x-7)

We move all terms to the left:

100(6x+7)-(10(x2+16x-7))=0

We add all the numbers together, and all the variables

-(10(+x^2+16x-7))+100(6x+7)=0

We multiply parentheses

-(10(+x^2+16x-7))+600x+700=0


We calculate terms in parentheses: -(10(+x^2+16x-7)), so:

10(+x^2+16x-7)

We multiply parentheses

10x^2+160x-70

Back to the equation:

-(10x^2+160x-70)


We add all the numbers together, and all the variables

600x-(10x^2+160x-70)+700=0

We get rid of parentheses

-10x^2+600x-160x+70+700=0

We add all the numbers together, and all the variables

-10x^2+440x+770=0

a = -10; b = 440; c = +770;
Δ = b2-4ac
Δ = 4402-4·(-10)·770
Δ = 224400
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:

$\sqrt{\Delta}=\sqrt{224400}=\sqrt{400*561}=\sqrt{400}*\sqrt{561}=20\sqrt{561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(440)-20\sqrt{561}}{2*-10}=\frac{-440-20\sqrt{561}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(440)+20\sqrt{561}}{2*-10}=\frac{-440+20\sqrt{561}}{-20}
$