Y-6=10x(x-7)

Solution for Y-6=10x(x-7) equation:

-6=10Y(Y-7)

We move all terms to the left:

-6-(10Y(Y-7))=0


We calculate terms in parentheses: -(10Y(Y-7)), so:

10Y(Y-7)

We multiply parentheses

10Y^2-70Y

Back to the equation:

-(10Y^2-70Y)


We get rid of parentheses

-10Y^2+70Y-6=0

a = -10; b = 70; c = -6;
Δ = b2-4ac
Δ = 702-4·(-10)·(-6)
Δ = 4660
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4660}=\sqrt{4*1165}=\sqrt{4}*\sqrt{1165}=2\sqrt{1165}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1165}}{2*-10}=\frac{-70-2\sqrt{1165}}{-20}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1165}}{2*-10}=\frac{-70+2\sqrt{1165}}{-20}
$