(x+10)(3x-5)=90

Solution for (x+10)(3x-5)=90 equation:

(x+10)(3x-5)=90

We move all terms to the left:

(x+10)(3x-5)-(90)=0

We multiply parentheses ..

(+3x^2-5x+30x-50)-90=0

We get rid of parentheses

3x^2-5x+30x-50-90=0

We add all the numbers together, and all the variables

3x^2+25x-140=0

a = 3; b = 25; c = -140;
Δ = b2-4ac
Δ = 252-4·3·(-140)
Δ = 2305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{2305}}{2*3}=\frac{-25-\sqrt{2305}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{2305}}{2*3}=\frac{-25+\sqrt{2305}}{6}
$