(10x+22)(7x+34)=90

Solution for (10x+22)(7x+34)=90 equation:

(10x+22)(7x+34)=90

We move all terms to the left:

(10x+22)(7x+34)-(90)=0

We multiply parentheses ..

(+70x^2+340x+154x+748)-90=0

We get rid of parentheses

70x^2+340x+154x+748-90=0

We add all the numbers together, and all the variables

70x^2+494x+658=0

a = 70; b = 494; c = +658;
Δ = b2-4ac
Δ = 4942-4·70·658
Δ = 59796
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:

$\sqrt{\Delta}=\sqrt{59796}=\sqrt{36*1661}=\sqrt{36}*\sqrt{1661}=6\sqrt{1661}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(494)-6\sqrt{1661}}{2*70}=\frac{-494-6\sqrt{1661}}{140}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(494)+6\sqrt{1661}}{2*70}=\frac{-494+6\sqrt{1661}}{140}
$