90=10x(x+7)

Solution for 90=10x(x+7) equation:

90=10x(x+7)

We move all terms to the left:

90-(10x(x+7))=0


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

10x(x+7)

We multiply parentheses

10x^2+70x

Back to the equation:

-(10x^2+70x)


We get rid of parentheses

-10x^2-70x+90=0

a = -10; b = -70; c = +90;
Δ = b2-4ac
Δ = -702-4·(-10)·90
Δ = 8500
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:

$\sqrt{\Delta}=\sqrt{8500}=\sqrt{100*85}=\sqrt{100}*\sqrt{85}=10\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10\sqrt{85}}{2*-10}=\frac{70-10\sqrt{85}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10\sqrt{85}}{2*-10}=\frac{70+10\sqrt{85}}{-20}
$